Beyond the Formula: A Systematic Review of How Senior High Students Make Sense of Derivatives
DOI:
https://doi.org/10.31980/mosharafa.v14i1.2922Keywords:
Konsep Turunan, Sekolah Menengah Atas, Telaah Pustaka Sistematis, Derivative Concepts, Senior High School, Systematic Literature ReviewAbstract
Turunan merupakan konsep dasar kalkulus yang memegang peranan penting dalam berbagai disiplin ilmu, termasuk fisika, teknik, dan ekonomi. Tetapi, banyak siswa yang mengalami kesulitan memahami dan menerapkan konsep-konsep turunan secara efektif. Penelitian ini bertujuan melakukan telaah pustaka sistematis tentang pengajaran konsep turunan dalam kalkulus di tingkat sekolah menengah atas. Penelitian Systematic literature review (SLR) ini disusun menggunakan lima komponen inti yaitu merumuskan pertanyaan penelitian, pendarian dan pemilihan literatur, pengumpulan data dan evaluasi kualitas, sintesis dan analisis data, serta pelaporan dan interpretasi. Telaah ini mengidentifikasi tantangan-tantangan utama yang dihadapi oleh siswa, mengeksplorasi strategi pengajaran yang efektif, serta peran sumber daya digital dalam meningkatkan pemahaman siswa. Telaah ini memberikan wawasan tentang praktik pengajaran yang dapat meningkatkan hasil belajar siswa dan mengidentifikasi bidang-bidang yang memerlukan penelitian lebih lanjut. Hasil telaah ini dapat memberikan kontribusi bagi pengembangan kurikulum dan metode pengajaran yang lebih efektif dalam pengajaran kalkulus di sekolah menengah atas.
Derivatives are fundamental concepts in calculus that play a vital role in various disciplines, including physics, engineering, and economics. However, many students struggle to understand and effectively apply derivative concepts. This study aims to conduct a systematic literature review on the teaching of derivative concepts in calculus at the high school level. This systematic literature review (SLR) is structured using five core components: formulating a research question, searching and selecting literature, collecting data and evaluating its quality, synthesizing and analyzing data, and reporting and interpreting. The review identifies key challenges faced by students, explores effective teaching strategies, and explores the role of digital resources in enhancing student understanding. It provides insights into teaching practices that can improve student learning outcomes and identifies areas requiring further research. The results of this review can contribute to the development of more effective curricula and teaching methods for calculus in high schools.
References
Afriansyah, E. A., & Turmudi, T. (2022). Prospective teachers’ thinking through realistic mathematics education based emergent modeling in fractions. Jurnal Elemen, 8(2), 605-618.
Ariza, A., Llinares, S., & Valls, J. (2015). Students’ Understanding of the Function-Derivative Relationship when Learning Economic Concepts. Mathematics Education Research Journal, 27(4), 615–635.
doi: 10.1007/s13394-015-0156-9
Asiala, M., Brown, A., DeVries, D., Dubinsky, E., & Mathews, D. (1997). A Framework for Research and Curriculum Development in Undergraduate Mathematics Education. In J. Kaput, A. H. Schoenfeld, & E. Dubinsky (Eds.), Research in collegiate mathematics education III, 1-32. American Mathematical Society.
Aydin, E., & Ubuz, B. (2014). Students' Understanding of the Derivative Concept: The Case of a High School in Turkey. International Journal of Mathematical Education in Science and Technology, 45(6), 841–854.
Aydın, U. & Ubuz, B (2014). Predicting Undergraduate Students' Mathematical Thinking about Derivative Concept: A Multilevel Analysis of Personal and Institutional Factors. Learning and Individual Differences, 32, 80-92
Baracat, D. E., Witkowski, F. M., & Cutri, R. (2013). Problem Based Learning in Multivariable Differential and Integral Calculus for Engineering Course. Proceedings of the 11th Latin American and Caribbean Conference for Engineering and Technology, 1-7.
Berger, M. (2013). Examining Mathematical Discourse to Understand in-Service Teachers’ Mathematical Activities. Pythagoras, 34(1).
http://dx.doi.org/10.4102/pythagoras.v34i1.197
Bergues. J. M, Casamayor. R, & Arada la de Acebes. D. (2019). Procedure to Introduce the Concept of The Derivative from A Meaningful Learning Perspective. 11th International Conference on Education and New Learning Technologies, 2584–2587.
Bingolbali, E. (2021). The Effects of Flipped Classroom Model on Students' Academic Achievement and Motivation in a Geometry Course. Eurasia Journal of Mathematics, Science and Technology Education, 17(1), em1928.
Bingolbali, E., & Ersozlu, Z. (2016). The Effect of Problem-Based Learning on Students’ Conceptual Understanding of Quadratic Functions. Eurasia Journal of Mathematics, Science and Technology Education, 12(1), 143–157.
Bingolbali, E., Monaghan, J., & Roper, T. (2007). Engineering Students’ Conceptions of the Derivative and Some Implications for Their Mathematical Education. International Journal of Mathematical Education in Science and Technology, 38(6), 763–777.
Borji, V., Martínez-Planell, R., & Trigueros, M. (2023). Students’ Geometric Understanding of Partial Derivatives and the Locally Linear Approach. Educational Studies in Mathematics, 115, 69–91
Brignardello-Petersen, R., Santesso, N., & Guyatt, G. H. (2024). Systematic Reviews of the Literature: An Introduction to Current Methods. American Journal of Epidemiology.
doi: 10.1093/aje/kwae232
Budinski, N., & Subramaniam, S. (2013). The First Derivative of an Exponential Function with the "White Box/Black Box" Didactical Principle and Observations with GeoGebra. European Journal of Contemporary Education, 4(2), 81-89.
https://doi.org/10.13187/EJCED.2013.4.81
Carlson, M., Madison, B., & West, R. (2010). The Calculus Concept Readiness (CCR) Instrument: Assessing Student Readiness for Calculus. arXiv preprint, arXiv:1010.2719v1.
Cervantes Salazar, M. (2011). Meaning the Derivative in a Modeling Context to Help Understanding. Journal of Mathematical Modelling and Application, 1(4), 20–32.
Chen, C. H., & Lin, Y. C. (2022). Impact of an AI-Assisted Feedback System on Students’ Conceptual Understanding and Problem-Solving Skills in Mathematics. Journal of Educational Technology & Society, 25(2), 112–125.
Chu, C. T. (2022). Lesson Plan: Differential Calculus through Applications. MINTUS – Beiträge zur mathematisch-naturwissenschaftlichen Bildung, 18, 287-305.
doi: 10.1007/978-3-658-36415-1_18
Chytas, C., van Borkulo, S., Drijvers, P., Barendsen, E., & Tolboom, J. (2024). Computational Thinking in Secondary Mathematics Education with GeoGebra: Insights from an Intervention in Calculus Lessons. Digital Experiences in Mathematics Education, 10(1), 87–110. https://doi.org/10.1007/s40751-024-00141-0
Dhlamini, Z. B., & Luneta, K. (2016). Exploration of the Levels of Mathematical Proficiency Displayed by Grade 12 Learners in Responses to Matric Examinations. International Journal of Educational Sciences, 13(2), 231–246.
doi:10.1080/09751122.2016.11890457
Edwards, H. M. (2007). Euler’s Definition of The Derivative. In Bulletin (New Series) of The American Mathematical Society, 44(4).
Emigh, P. J., & Manogue, C. A. (2024). Concept Image Framework for Derivatives from Contour Graphs. Physical Review Physics Education Research, 20(2). doi: 10.1103/PhysRevPhysEducRes.20.020140
English, L. D., & Watson, J. M. (2018). Mathematical Modeling in STEM Education: A Systematic Review. Educational Studies in Mathematics, 98(3), 301-326. doi: 10.1007/s10649-018-9824-2
García-García, J., & Dolores-Flores, C. (2021). Pre-University Students’ Mathematical Connections when Sketching the Graph of Derivative and Antiderivative Functions. Mathematics Education Research Journal, 33(1). doi: 10.1007/s13394-019-00286-x
Handhika, J., & Sasono, M. (2021). Using of GeoGebra Software to Improve Understanding of Vector and Kinematic Concepts in Online Physics Course. Jurnal Pendidikan Fisika dan Keilmuan, 7(1), 1–12.
https://doi.org/10.25273/jpfk.v7i1.8619
Grant, M. R., Crombie, W., Enderson, M., & Cobb, N. (2016). Polynomial Calculus: Rethinking the Role of Calculus in High Schools. International Journal of Mathematical Education in Science and Technology, 47(6), 823–836. doi: 10.1080/0020739X.2015.1133851
Haciomeroglu, E. S., & Andreasen, J. B. (2013). Exploring Calculus with Dynamic Mathematics Software. Mathematics and Computer Education, 47(1), 6-18.
Hallal, R., Pinheiro, N. A. M., Oliveira, R., Ciappina, J. R., & Alvaristo, E. F. (2020). O Ensino de Matemática e o Software GeoGebra. Apresentando Potencialidades Dessa Relação Como Recurso Para o Ensino de Derivada. Revista Espacios, 41(24), 25–34.
Hancock, E., Franco, L., Bagley, S., & Karakok, G. (2021). A Holistic Approach to Supporting Student-Centered Pedagogy: Navigating Co-Requisite Calculus I. PRIMUS, 31(8), 832-851. doi: 10.1080/10511970.2020.1802794
Hashemi, N., Abu, M. S., Kashefi, H., Mokhtar, M., & Rahimi, K. (2015). Designing Learning Strategy to Improve Undergraduate Students' Problem Solving in Derivatives and Integrals: A Conceptual Framework. Eurasia Journal of Mathematics, Science and Technology Education, 11(2), 227-238.
https://doi.org/10.12973/EURASIA.2015.1318A
Herbert, S., & Pierce, R. (2012). Revealing Educationally Critical Aspects of Rate. Educational Studies in Mathematics, 81(1), 85–101.
Hernandez-Martinez, P., Rogovchenko, S., Rogovchenko, Y., & Treffert-Thomas, S. (2024). “The theorem says…”: Engineering Students making Meaning of Solutions to Ordinary Differential Equations. Journal of Mathematical Behavior, 73.
doi: 10.1016/j.jmathb.2023.101116
Hong, Y. & Thomas, M. (2013). Graphical Construction of a Local Perspective. In A. Lindmeier, & A. Heinze (Eds.), Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education, 3, pp. 81–90. Kiel: PME.
Idowu, E. (2024). Personalized Learning: Tailoring Instruction to Individual Student Needs. Preprints, 2024110863. doi: 10.20944/preprints202411.0863.v1
Inthanon, W., & Wised, S. (2024). Tailoring Education: A Comprehensive Review of Personalized Learning Approaches Based on Individual Strengths, Needs, Skills, and Interests. Journal of Educational Learning and Research, 3(2). doi: 10.60027/jelr.2024.779
Jun-xiang, K. (2006). How to Teach the Concept of Derivative. Shayang Teachers College.
Kendal, M., & Stacey, K. (1999). The Impact of Teacher Privileging on Learning Differentiation with Technology. In Proceedings of the 23rd Annual Conference of the International Group for the Psychology of Mathematics Education, 3, 129–136.
Kertil, M., & Dede, H. G. (2022). Promoting Prospective Mathematics Teachers' Understanding of Derivative across Different Real-life Contexts. International Journal for Mathematics Teaching and Learning, 23(1), 1-24.
Laja, Y. P. W. (2022). Analisis Kesulitan Mahasiswa Pendidikan Matematika dalam Menyelesaikan Soal Limit Trigonometri. Mosharafa: Jurnal Pendidikan Matematika, 11(1), 37-48. https://doi.org/10.31980/mosharafa.v11i1.685
Lan, X., & Ying, Z. (2021). Teaching Derivative Concept Using 6 Questions Cognitive Model. Journal of Didactic Mathematics, 1(3), 127–137. doi: 10.34007/jdm.v1i3.371
Lim, K. Y., & Lee, P. C. (2012). Connecting Calculus and Physics: An Instructional Intervention for Improving Students' Understanding of Derivatives. International Journal of Science and Mathematics Education, 10(4), 841–862.
Lim, S. C., & Choy, D. (2016). The Effect of Flipped Classroom Instruction on Students' Conceptual Understanding of Mathematics. Journal of Computer Assisted Learning, 32(3), 213–225.
Lim, S. C., & Teo, B. H. (2009). Developing Mathematical Communication Skills through Student-Centred Learning. In J. T. E. B. C. L. & T. L. P. (Eds.), Mathematics education: The Singapore experience, 101–119. World Scientific Publishing Co. Pte. Ltd.
Lim, S. Y. (2015). A Study on the Relationship between Procedural Fluency and Conceptual Understanding of Derivative among High School Students in Singapore. Journal of Science and Mathematics Education in Southeast Asia, 38(1), 22–45.
Lin, R. M., Mottershead, J. E., & Ng, T. Y. (2020). A State-of-the-Art Review on Theory and Engineering Applications of Eigenvalue and Eigenvector Derivatives. In Mechanical Systems and Signal Processing, 138. Academic Press.
doi: 10.1016/j.ymssp.2019.106536
Listiawati, E., Juniati, D., & Ekawati, R. (2025). Building an Understanding of Sketching Function Derivative Graphs through the APOS Approach. Edelweiss Applied Science and Technology, 9(2), 555–566.
doi: 10.55214/25768484.v9i2.4521
Little, C. (2011). Approaches to Calculus Using Geogebra. In: Bu, L., Schoen, R. (eds) Model-Centered Learning. Modeling and Simulations for Learning and Instruction, 6. SensePublishers.
https://doi.org/10.1007/978-94-6091-618-2_14
Luneta, K., & Makonye, P. J. (2010). Learner Errors and Misconceptions in Elementary Analysis: A Case Study of a Grade 12 Class in South Africa. Acta Didactica Napocensia, 3(3), 35-46.
Machisi, E. (2024). An Analysis of Calculus Application Questions in Grade 12 Mathematics Exams in South Africa. Eurasia Journal of Mathematics, Science and Technology Education, 20(10). doi: 10.29333/ejmste/15431
Meldi, N. F., Khoriyani, R. P., Susanti, W. R., Ahmad, D., & Rif'at, M. (2022). Implementasi Teknologi Digital dalam Perkuliahan Matakuliah Kalkulus Integral dalam Penyelesaian Luas Daerah antar Kurva. Jurnal Alwatzikhoebillah: Kajian Islam, Pendidikan, Ekonomi, Humaniora, 8(2), 139–148.
https://doi.org/10.37567/alwatzikhoebillah.v8i2.1506
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).
doi: 10.29333/ejmste/14380
Mokhtar, M. Z., Tarmizi, R. A., Ayub, A. F. M., & Nawawi, M. (2013). Motivation and Performance in Learning Calculus through Problem-Based Learning. International Journal of Asian Social Science, 3(9), 1999-2005.
Moru, E. K. (2020). An APOS Analysis of University Students’ Understanding of Derivatives: A Lesotho Case Study. African Journal of Research in Mathematics, Science and Technology Education, 24(2), 279–292. doi: 10.1080/18117295.2020.1821500
Mufidah, A. D., Suryadi, D., & Rosjanuardi, R. (2019). Teacher Images on the Derivatives Concept. Journal of Physics: Conference Series, 1157(4). doi: 10.1088/1742-6596/1157/4/042119
Mutolo, S. (2018). The Role of Physics Context in Developing Conceptual Understanding of Derivatives. Journal of Physics Education, 15(3), 112–125.
Mutolo, S. (2022). Physics Education Research and the Use of Technology. Disertasi atau makalah konferensi.
Ndlovu, M., Wessels, D., & De Villiers, M. (2011). An Instrumental Approach to Modelling the Derivative in Sketchpad. Pythagoras, 32(2), 52.
https://doi.org/10.4102/PYTHAGORAS.V32I2.52
Neves, R. (2019). Teaching Physics in Science, Technology, Engineering and Mathematics Education Contexts with Interactive Computational Modelling. AIP Conference Proceedings, 2116(1), 030016. doi: 10.1063/1.5114426
Nuraeni, R., & Siregar, H. M. (2024). Eksplorasi Pembelajaran Kalkulus Integral dengan Menggunakan Teknologi. Plusminus: Jurnal Pendidikan Matematika, 4(1), 83-94. https://doi.org/10.31980/plusminus.v4i1.1526
Pangesti, K. I., & Triyanta. (2022). STEM Project Topics Relevant to the Physics Curriculum at High School Level. Journal of Physics: Conference Series, 2243(1), 012111. doi: 10.1088/1742-6596/2243/1/012111
Park, J. (2013). Is the Derivative a Function? If so, How Do Students Talk about it? International Journal of Mathematical Education in Science and Technology, 44(5), 624–640.
https://doi.org/10.1080/0020739X.2013.795248
Parzysz, B. (2006). Geometrical Reasoning and Visualization. In J. Novotná, H. Moraová, M. Krátká, & V. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education, 4, 289–296. Prague: PME.
Puspitasari, N., Sofyan, D., Handriani, R. T. S., & Maharani, R. P. (2023). Improving Junior High School Students' Ability to Ask Mathematical Problems through the Use of Geogebra-Based Learning Media. Mosharafa: Jurnal Pendidikan Matematika, 12(4), 937-946. https://doi.org/10.31980/mosharafa.v12i4.1203
Roh, K. H. (2010). An Empirical Study of Students’ Understanding of a Logical Structure in the Definition of Limit via the Ε-Strip Activity. Educational Studies in Mathematics, 73(3), 263–279. https://doi.org/10.1007/s10649-009-9210-4
Roorda, G., Vos, P., & Goedhart, M. (2007). The Concept of Derivative in Modelling and Applications. Mathematical modelling: Education, engineering and economics, 288-293.
Roslina, R., Samsudin, A., & Liliawati, W. (2022). Effectiveness of Project Based Learning Integrated STEM in Physics Education (STEM-PJBL): Systematic literature review (SLR). Phenomenon: Jurnal Pendidikan MIPA, 12(1), 1-22. doi: 10.21580/phen.2022.12.1.11722
Schmiedmayer, B., & Kresse, G. (2024). Derivative Learning of Tensorial Quantities—Predicting Finite Temperature Infrared Spectra from First Principles. Journal of Chemical Physics, 161(8).
doi: 10.1063/5.0217243
Sharma, P. (2024). Revolutionizing Math Education: The Power of Personalized Learning. International Journal for Multidisciplinary Research, 6(2). doi: 10.36948/ijfmr.2024.v06i02.16508
Shatila, H. G. (2015). Students' Conceptual Understanding of Derivatives in Freshmen Calculus. (c2015). Doctoral dissertation, Lebanese American University.
Sherley, S. E. F., Prabakaran, R., & Lakshmi, S. (2024). Student-Centered Learning in the Digital Age. In Digital Transformation in Higher Education (pp. 25-40). CRC Press. doi: 10.1201/9781003469315-2
Sungkono, S., Apiati, V., & Santika, S. (2022). Media pembelajaran berbasis teknologi augmented reality. Mosharafa: Jurnal Pendidikan Matematika, 11(3), 459-470. https://doi.org/10.31980/mosharafa.v11i3.737
Szydlik, J. E. (2000). Mathematical Beliefs and Conceptual Understanding of the Limit of a Function. In Journal for Research in Mathematics Education, 31(3).
Thomas, A. (2023). The Use of Graphing Applications in Calculus and Physics Education. American Journal of Physics, 91(4), 215–228.
Thompson, A. G., & Senk, S. L. (2021). Real-World Applications of Calculus in STEM Fields: An Educational Perspective. Journal of Mathematical Behavior, 63, 100876. doi: 10.1016/j.jmathb.2021.100876
Toromade, A. O., Orakwe, C. U., & Okonkwo, C. A. (2024). Equity-Centered Adaptive Learning (ECAL) in Mathematics: Personalizing Education for Underrepresented Groups. International Journal of Applied Research in Social Sciences, 6(11). doi: 10.51594/ijarss.v6i11.1693
Trigueros, M., Martínez-Planell, R., & McGee, D. (2018). Student Understanding of the Relation between Tangent Plane and the Total Differential of Two-Variable Functions. International Journal of Research in Undergraduate Mathematics Education, 4(1), 181–197.
Trigueros, M., Martínez-Planell, R., & Borji, V. (2023). Development of the Differential Calculus Schema for Two-Variable Functions. Prosiding konferensi INDRUM.
Ubuz, B. (2007). Interpreting a Graph and Constructing its Derivative Graph: Stability and Change in Students’ Conceptions. International Journal of Mathematical Education in Science and Technology, 38(5), 609–637. doi: 10.1080/00207390701359313
Uden, L., Sulaiman, F., Ching, S. C., & Rosales, J. (2023). Integrated Science, Technology, Engineering, and Mathematics Project-Based Learning for Physics Learning from Neuroscience Perspectives. Frontiers in Psychology, 14, 1136246.
doi: 10.3389/fpsyg.2023.1136246
Uwurukundo, M. S., Maniraho, J. F., & Tusiime, M. (2020). GeoGebra Integration and Effectiveness in the Teaching and Learning of Mathematics in Secondary Schools: A Review of Literature. African Journal of Educational Studies in Mathematics and Sciences, 16(1), 1–11.
https://doi.org/10.4314/ajesms.v16i1.1
Verhoef, N. C., Coenders, F., Pieters, J. M., van Smaalen, D., & Tall, D. O. (2015). Professional Development through Lesson Study: Teaching the Derivative using GeoGebra. Professional Development in Education, 41(1), 109–126.
doi: 10.1080/19415257.2014.886285
Vetier, G. (2005). Exploring the Limit Concept with Dynamic Geometry Software. The International Journal for Technology in Mathematics Education, 12(1), 35–42.
Villavicencio, J.-A. F. (2023a). Error Analysis in Basic Calculus: A Basis for Improving Teaching Strategies. International Journal of Scientific and Research Publications, 13(8), 156–162. doi: 10.29322/ijsrp.13.08.2023.p14019
Villavicencio, J.-A. F. (2023b). Error Analysis in Basic Calculus: A Basis for Improving Teaching Strategies. International Journal of Scientific and Research Publications, 13(8), 156–162. doi: 10.29322/ijsrp.13.08.2023.p14019
Weigand, H. G. (2014). A Discrete Approach to the Concept of Derivative. ZDM - International Journal on Mathematics Education, 46(4), 603–619. doi: 10.1007/s11858-014-0595-x
Yuliandari, T. M., Putri, A., & Rosmansyah, Y. (2023). Digital Transformation in Secondary Schools: A Systematic Literature Review. In IEEE Access, 11, pp. 90459–90476. Institute of Electrical and Electronics Engineers Inc.
doi: 10.1109/ACCESS.2023.3306603
Zandieh, M. (2000).
“A Theoretical Framework for Analyzing Student Understanding of the Derivative.” In M. Dubinsky, A. Schoenfeld, & J. Kaput (Eds.), Research in Collegiate Mathematics Education IV, 8, pp. 103–127. American Mathematical Society.
Zhang, Y. (2024). The Application of Calculus in Physics. Science and Technology of Engineering, Chemistry and Environmental Protection, 2(4), 45-52. doi: 10.61173/akrb7f68
Zhilmagambetova, R., Kopeyev, Z., Mubarakov, A., & Alimagambetova, A. Z. (2023). The Role of Adaptive Personalized Technologies in the Learning Process. International Journal of Virtual and Personal Learning Environments, 14(1).
doi: 10.4018/ijvple.324079
Ziatdinov, R., & Valles, J. R. (2022). Synthesis of Modeling, Visualization, and Programming in GeoGebra as an Effective Approach for Teaching and Learning STEM Topics. Mathematics, 10(3), 398. https://doi.org/10.3390/math10030398
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