Application of Discovery Learning Model to Improve Students’ Conceptual Understanding on Algebraic Function Derivatives

Palwina Machrani; Rahmat Badawi; Rama Nida Siregar

doi:10.22460/jiml.v8i4.30089

Authors

Palwina Machrani UIN Syekh Ali Hasan Ahmad Addary, Padangsidimpuan, Indonesia
Rahmat Badawi UIN Syekh Ali Hasan Ahmad Addary, Padangsidimpuan, Indonesia
Rama Nida Siregar UIN Syekh Ali Hasan Ahmad Addary, Padangsidimpuan, Indonesia https://orcid.org/0000-0002-8285-7096

DOI:

https://doi.org/10.22460/jiml.v8i4.30089

Keywords:

Conceptual Understanding , Algebraic Function Derivatives , Discovery Learning , Senior High School

Abstract

Understanding the derivative of algebraic functions remains challenging for many students, particularly in linking fundamental concepts such as limits, rates of change, and the geometric interpretation of tangent slopes. These persistent difficulties indicate that conventional instruction has not sufficiently supported students in constructing deep conceptual knowledge. This study aims to analyze the effect of the Discovery Learning model on improving students’ conceptual understanding of algebraic function derivatives. A quasi-experimental method with a Nonequivalent Control Group Design was employed, involving two Grade XII classes at SMA Negeri 1 Batangtoru. The experimental class received instruction using Discovery Learning, while the control class received direct instruction. Data were obtained through conceptual understanding tests, student activity observations, and teacher observations. The implementation of Discovery Learning followed stages of stimulation, problem identification, data collection, verification, and generalization, enabling students to explore derivative concepts through graphical, numerical, and symbolic representations. The results show that the experimental class achieved a higher mean posttest score (82.6) than the control class (73.3). A t-test yielded a significance value of 0.001, indicating a significant difference between the two groups. These findings demonstrate that Discovery Learning enhances students’ conceptual understanding by promoting active exploration, reasoning, and pattern recognition. In conclusion, Discovery Learning is effective for teaching derivatives of algebraic functions and offers strong potential to support concept-based mathematics instruction at the secondary school level.

References

Astuti, S. A. B., Siregar, R. N., & Rangkuti, R. K. (2025). Analysis of Students’ Mathematical Critical Thinking in Solving Function Derivative Problems based on Gender Differences. (JIML) Journal of Innovative Mathematics Learning, 8(1), 188–199. https://doi.org/10.22460/JIML.V8I1.27166

Byerley, C. (2019). Calculus students’ fraction and measure schemes and implications for teaching rate of change functions conceptually. The Journal of Mathematical Behavior, 55, 100694. https://doi.org/10.1016/J.JMATHB.2019.03.001

Feudel, F., & Biehler, R. (2021). Students’ Understanding of the Derivative Concept in the Context of Mathematics for Economics. Journal Fur Mathematik-Didaktik, 42(1), 273–305. https://doi.org/10.1007/S13138-020-00174-Z/FIGURES/6

Gopalan, M., Rosinger, K., & Ahn, J. Bin. (2020). Use of Quasi-Experimental Research Designs in Education Research: Growth, Promise, and Challenges. Review of Research in Education, 44(1), 218–243. https://doi.org/10.3102/0091732X20903302

Gribbons, B., & Herman, J. (1996). True and Quasi-Experimental Designs. Practical Assessment, Research, and Evaluation, 5(1). https://doi.org/10.7275/FS4Z-NB61

Hafeez, M. (2021). Systematic Review on Modern Learning Approaches, Critical Thinking Skills and Students Learning Outcomes. Indonesian Journal of Educational Research and Review, 4(1), 167–178. https://doi.org/10.23887/IJERR.V4I1.33192

Hasnunidah, N., Fadhila, S., Yolida, B., Nadya, M., & Maulina, D. (2024). Optimizing Discovery Learning to Enhance HOTS: Why Use Argumentative Worksheets? Jurnal Penelitian Pendidikan IPA, 10(12), 10348–10358. https://doi.org/10.29303/JPPIPA.V10I12.9412

Hekimoglu, S., & Sloan, M. (2005). A Compendium of Views on the NCTM Standards. Mathematics Educator, 15(1), 35–43.

Hermann, G. (1969). Learning by discovery. Journal of Experimental Education, 38(1), 58–72. https://doi.org/10.1080/00220973.1969.11011167;CTYPE:STRING:JOURNAL

Hoidn, S. (2017). Constructivist Foundations and Common Design Principles of Student-Centered Learning Environments. Student-Centered Learning Environments in Higher Education Classrooms, 23–103. https://doi.org/10.1057/978-1-349-94941-0_2

Huda, N., & Amanu, B. A. (2023). Penerapan model discovery learning berbantukan LKPD untuk meningkatkan pemahaman konsep pada materi integral fungsi aljabar. http://prosiding.senpika.ulm.ac.id/index.php/senpika/article/view/5

Indrapangastuti, D., Dwi Surjono, H., Endri Yanto, B., & Author, C. (2021). Effectiveness of the Blended Learning Model to Improve Students’ Achievement of Mathematical Concepts. Journal of Education and E-Learning Research, 8(4), 423–430. https://doi.org/10.20448/journal.509.2021.84.423.430

Kamaluddin, M., & Widjajanti, D. B. (2019). The Impact of Discovery Learning on Students’ Mathematics Learning Outcomes. Journal of Physics: Conference Series, 1320(1), 012038. https://doi.org/10.1088/1742-6596/1320/1/012038

Krishnan, P. (2019). A review of the non-equivalent control group post-test-only design. Nurse Researcher, 26(2), 37–40. https://doi.org/10.7748/NR.2018.E1582

Kristiyajati, A., & Wijaya, A. (2019). The Effectiveness of Visualization of Proofs in Learning Mathematics by Using Discovery Learning Viewed from Conceptual Understanding. Southeast Asian Mathematics Education Journal, 9(1), 37–44. https://doi.org/10.46517/SEAMEJ.V9I1.72

Kurino, Y. D., Herman, T., Turmudi, T., Yonanda, D. A., & Haryanti, Y. D. (2024). Enhancing Mathematical Problem-Solving Skills Through Flipped Classrooms and Discovery Learning: A Resilience-Based Approach for Elementary Students. AL-ISHLAH: Jurnal Pendidikan, 16(4), 5399–5408. https://doi.org/10.35445/ALISHLAH.V16I4.6243

Legi Adilawati, F., Siti Nur Atiqoh, K., Eva Musyrifah, dan, Atiqoh, S. N., Musyrifah, dan E., & Kemampuan Berpikir Aljabar Ditinjau dari Gaya Kognitif Siswa, A. (2025). Analisis Kemampuan Berpikir Aljabar Ditinjau dari Gaya Kognitif Siswa. Euler : Jurnal Ilmiah Matematika, Sains Dan Teknologi, 13(2), 238–246. https://doi.org/10.37905/EULER.V13I2.32947

McKeachie, W. J. (2006). Procedures and Techniques of Teaching: A Survey of Experimental Studies. The American College: A Psychological and Social Interpretation of the Higher Learning., 312–364. https://doi.org/10.1037/11181-008

Mkhatshwa, T. P. (2024). Best practices for teaching the concept of the derivative: Lessons from experienced calculus instructors. Eurasia Journal of Mathematics, Science and Technology Education, 20(4), em2426. https://doi.org/10.29333/EJMSTE/14380

Muhammad, R. R., Lawson, D., Aslam, F., & Crawford, M. (2022). The Scientific Approach of The Indonesian 2013 Curriculum: A Comparison with Other Active Learning Strategies in Mathematics. Journal of Research in Science, Mathematics and Technology Education , 5(2), 155–171. https://doi.org/10.31756/JRSMTE.523

Mulyani, S., & Siregar, R. N. (2025). Analysis of Students’ Mathematical Understanding of Derivatives Algebraic Function on Islamic Boarding High School. (JIML) Journal of Innovative Mathematics Learning, 8(1), 173–187. https://doi.org/10.22460/JIML.V8I1.27159

Ningsih, E. L. C., & Jayanti, U. N. A. D. (2022). Discovery Blended Learning in Biology: Its Effectiveness on Self-Efficacy and Student Learning Outcomes in the New Normal Era. Formatif: Jurnal Ilmiah Pendidikan MIPA, 12(2), 147–160. https://doi.org/10.30998/FORMATIF.V12I2.13748

Nurhidayat, W., Surahman, E., & Sujarwanto, E. (2023). The Effect of Conceptual Understanding Procedures Learning Model on Students’ Higher Level Thinking Skills. JPI (Jurnal Pendidikan Indonesia), 12(2), 386–394. https://doi.org/10.23887/JPIUNDIKSHA.V12I2.58709

Pacaci, C., Ustun, U., & Ozdemir, O. F. (2024). Effectiveness of conceptual change strategies in science education: A meta-analysis. Journal of Research in Science Teaching, 61(6), 1263–1325. https://doi.org/10.1002/TEA.21887;ISSUE:ISSUE:DOI

Palinussa, A. L., Lakusa, J. S., & Moma, L. (2023). Comparison of Problem-Based Learning and Discovery Learning To Improve Students’ Mathematical Critical Thinking Skills. Formatif: Jurnal Ilmiah Pendidikan MIPA, 13(1). https://doi.org/10.30998/FORMATIF.V13I1.15205

Rodríguez-Nieto, C. A., & Moll, V. F. (2025). Mathematical connections promoted in multivariable calculus’ classes and in problems-solving about vectors, partial and directional derivatives, and applications. Eurasia Journal of Mathematics, Science and Technology Education, 21(4), em2619. https://doi.org/10.29333/EJMSTE/16187

Sakdiah, S., & Siregar, R. N. (2025). Analysis of Students’ Errors in Solving Algebraic Function Limit Problems based on Bloom’s Taxonomy. (JIML) Journal of Innovative Mathematics Learning, 8(1), 160–172. https://doi.org/10.22460/JIML.V8I1.27152

Salcedo, D., Regan, J., Aebersold, M., Lee, D., Darr, A., Davis, K., & Berrocal, Y. (2022). Frequently Used Conceptual Frameworks and Design Principles for Extended Reality in Health Professions Education. Medical Science Educator 2022 32:6, 32(6), 1587–1595. https://doi.org/10.1007/S40670-022-01620-Y

Simamora, R. E., Saragih, S., & Hasratuddin. (2019). Improving Students’ Mathematical Problem Solving Ability and Self-Efficacy through Guided Discovery Learning in Local Culture Context. International Electronic Journal of Mathematics Education, 14(1), 61–72. https://doi.org/10.12973/iejme/3966

Siregar, R., & Siregar, R. N. (2025). Analysis of Students’ Mathematical Problem-Solving Ability on Senior High School – Case on Function Derivative Material. (JIML) Journal of Innovative Mathematics Learning, 8(1), 148–159. https://doi.org/10.22460/JIML.V8I1.27134

Sweller, J. (2021). The Role of Evolutionary Psychology in Our Understanding of Human Cognition: Consequences for Cognitive Load Theory and Instructional Procedures. Educational Psychology Review 2021 34:4, 34(4), 2229–2241. https://doi.org/10.1007/S10648-021-09647-0

Tong, D. H., Uyen, B. P., & Ngan, L. K. (2022). The effectiveness of blended learning on students’ academic achievement, self-study skills and learning attitudes: A quasi-experiment study in teaching the conventions for coordinates in the plane. Heliyon, 8(12), e12657. https://doi.org/10.1016/j.heliyon.2022.e12657