Deskripsi Kemampuan Generalisasi Matematis Siswa pada Materi Eksponen melalui Pembelajaran PACE
DOI:
https://doi.org/10.31851/indiktika.v8i2.21897Keywords:
Mathematical Generalization Ability, PACE Model, ExponentAbstract
The ability to generalize in mathematics helps in recognizing patterns and creating general rules. The project, activity, cooperative learning, exercise (PACE) model was chosen because it encourages students to actively build their own knowledge. This study aims to describe students' mathematical generalization abilities on exponent material after participating in learning using the PACE model. The research used a quantitative descriptive method with the subjects being students of class X.3 at SMAN 2 Indralaya Utara. Data were collected through essay tests that had been rated highly valid by three validators, and then analyzed descriptively based on generalization ability indicators. The results showed that students' mathematical generalization ability fell into the medium category. The perception of generality indicator had the highest achievement percentage, while manipulation of generality was the lowest. The findings show that students have been able to recognize patterns in exponent material, but still face difficulties when using the general form to solve advanced problems. This study provides an overview of the achievement of each indicator of students' mathematical generalization abilities in exponent material after learning using the PACE model.
References
Aprilita, P., Mirza, A., & Nursangaji, A. (2016). Analisis Kemampuan Generalisasi Matematis Siswa di Kelas VII Sekolah Menengah Pertama. Jurnal Pendidikan Dan Pembelajaran Khatulistiwa (JPPK), 5(10), 1–10. https://doi.org/10.26418/jppk.v5i10.16777
Assaibin, M., Wahyuddin, & Husain, R. (2020). Kemampuan Berpikir Kreatif Dan Komunikasi Matematis Melalui Model PACE (Project activity cooperative exercise) Siswa Kelas VII SMP Negeri 1 Polewali. Genta Mulia, XI(2), 56–69. https://doi.org/10.61290/gm.v11i2.262
Azizah, P. N., Maharani, S., & Suprapto, E. (2022). Kemampuan Generalisasi Siswa SMK dalam Menyelesaikan Masalah Barisan dan Deret berdasarkan Brain Dominance. Jurnal Pendidikan Dan Konseling, 4(4), 2425–2433. https://doi.org/10.31004/jpdk.v4i4.5809
Dewi, M. D., & Izzati, N. (2020). Pengembangan Media Pembelajaran PowerPoint Interaktif Berbasis RME Materi Aljabar Kelas VII SMP. Delta: Jurnal Ilmiah Pendidikan Matematika, 8(2), 217. https://doi.org/10.31941/delta.v8i2.1039
Dwirahayu, G., Kustiawati, D., & Bidari, I. (2018). Pengaruh Habits Of Mind terhadap Kemampuan Generalisasi Matematis. JPPM (Jurnal Penelitian Dan Pembelajaran Matematika), 11(2), 91–104. https://doi.org/10.30870/jppm.v11i2.3757
Elly S, A., & Refianti, R. (2022). Kemampuan Generalisasi Matematis Melalui Pendekatan Keterampilan Metakognitif di SMP Negeri Megang Sakti. Jurnal Perspektif Pendidikan, 16(1), 44–51. https://doi.org/10.31540/jpp.v16i1.1569
Fitriani, K. I. N., Dwinata, A., & Putri, N. H. S. (2024). Peningkatan Kemampuan Penalaran Matematis menggunakan Model Pembelajaran PACE dengan Konteks Kemaritiman pada Siswa Kelas VIII SMP. Symmetry | Pasundan Journal of Research in Mathematics Learning and Education, 9(2), 246–252. https://doi.org/10.23969/symmetry.v9i2.16319
Fitriyah, I. M., Arrifadah, Y., & Lailiyah, S. (2021). Semiotics of mathematics problem-solving in Mason’s generalization. Jurnal Riset Pendidikan Matematika, 8(1), 1–21. https://doi.org/10.21831/jrpm.v8i1.39621
Hadi, S., Dolk, M., Kamaliyah, & Hidayanto, T. (2025). Mathematical reasoning: How students learn mathematics? Journal on Mathematics Education, 16(3), 937–954. https://doi.org/10.22342/jme.v16i3.pp937-954
Hartri, L., & Hakim, D. L. (2023). Kemampuan Generalisasi Matematis Siswa SMP pada Materi Segiempat dan Segitiga. Jurnal Pendidikan Dan Konseling, 5(2), 3082–3092. https://doi.org/10.31004/jpdk.v5i2.13606
Huda, S., Mujib, A., & Ramdhani, S. (2024). Analisis Kemampuan Penalaran Matematis Siswa Kelas VII Berdasarkan Gaya Kognitif Field Independent dan Dependent. Jurnal Didaktika Pendidikan Dasar, 8(3), 1153–1176. https://doi.org/10.26811/didaktika.v8i3.1619
Husnuddu’a, A. U., Sarjana, K., Kurniawan, E., & Soeprianto, H. (2022). Pengaruh Kecenderungan Berpikir Kritis terhadap Kemampuan Generalisasi Matematis pada Materi Barisan dan Deret Siswa Kelas XII SMA Negeri 1 Narmada. Journal of Mathematics Education and Application, 2(4), 988–1001. https://doi.org/10.29303/griya.v2i4.248
Jackson, J. L., & Stenger, C. L. (2024). Methods of Explicitly Teaching Generalization in the Mathematics Classroom and Indicators of Success: A Systematic Review. International Journal of Education in Mathematics, Science and Technology (IJEMST), 12(4), 1109–1126. https://doi.org/10.46328/ijemst.4171
Junengsih, J., & Sutirna. (2022). Analisis Kesulitan Siswa dalam Mengerjakan Soal pada materi Eksponen. Jurnal Ilmiah Dikdaya, 12(1), 28–32. https://doi.org/10.33087/dikdaya.v12i1.303
Karabulut, A., & Özmen, E. R. (2018). Effect of “understand and solve!” strategy instruction on mathematical problem solving of students with mild intellectual disabilities. International Electronic Journal of Elementary Education, 11(2), 77–90. https://doi.org/10.26822/iejee.2018245314
Khusuma, D., Masykur, R., & Andriani, S. (2021). Model Pembelajaran Pace dan Self Efficacy: Dampak terhadap Kemampuan Pemecahan Masalah Matematis. AdMathEdu, 11(2), 121–136. https://doi.org/10.12928/admathedu.v11i2.22368
Lee, C. (1998). An Assessment Of the PACE Strategy for An Introductory Statistics Course. https://www.researchgate.net/publication/255044747
Lestari, A. C., & Annizar, A. M. (2020). Proses Berpikir Kritis Siswa dalam Menyelesaikan Masalah PISA Ditinjau dari Kemampuan Berpikir Komputasi. Jurnal Kiprah, 8(1), 46–55. https://doi.org/10.31629/kiprah.v8i1.2063
Marwiyah, S., Pujiastuti, H., & Sukirwan. (2020). Profil Kemampuan Penalaran Matematis Siswa ditinjau dari Gaya Belajar V-A-K pada Materi Bangun Ruang Sisi Datar. Teorema: Teori Dan Riset Matematika, 5(2), 294–307. https://doi.org/10.25157/teorema.v5i2.3738
Mason, J. (1996). Expressing Generality and Roots of Algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to Algebra: Perspectives for Research and Teaching (pp. 65–86). Kluwer Academic Publishers.
Mata-Pereira, J., & da Ponte, J. P. (2017). Enhancing students’ mathematical reasoning in the classroom: teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96(2), 169–186. https://doi.org/10.1007/s10649-017-9773-4
Medová, J., Bulková, K. O., & Čeretková, S. (2020). Relations between generalization, reasoning and combinatorial thinking in solving mathematical open-ended problems within mathematical contest. Mathematics, 8(12), 1–20. https://doi.org/10.3390/math8122257
Muslimah, A., Pujiastuti, H., Mustafa, A. N., & Novaliyosi. (2025). Analisis Kemampuan Generalisasi Matematis Siswa SMP Kota Cilegon. Media Pendidikan Matematika, 13(2), 797–807. https://doi.org/10.33394/mpm.v13i2.18458
Naraswari, T. P., Kusmayadi, T. A., & Fitriana, L. (2023). Students’ Mathematical Generalization in Solving Numeracy Problems. Jurnal Penelitian Dan Pengembangan Pendidikan, 7(3), 533–542. https://doi.org/10.23887/jppp.v7i3.66888
NCTM. (2000). Principles and Standards for School Mathematics. National Council of Teachers of Mathematics.
Pradana, D. A. Y., & Murtiyasa, B. (2020). Kemampuan siswa menyelesaikan masalah berbentuk soal cerita sistem persamaan linear ditinjau dari kemampuan penalaran. Pythagoras: Jurnal Pendidikan Matematika, 15(2). https://doi.org/10.21831/pg.v15i2.35419
Pratama, M. F. R., Dewi, N. R., & Wijayanti, K. (2024). Keefektifan Model Pembelajaran PACE Berbantuan Google Classroom terhadap Kemampuan Penalaran Matematis Siswa pada Materi Phytagoras. Jurnal Studi Guru Dan Pembelajaran, 7(2), 759–769. https://doi.org/10.30605/jsgp.7.2.2024.4355
Putra, Z. R. A., & Oktaviane, D. A. K. (2022). Analisis Hasil Belajar Siswa pada Materi Eksponensial berdasarkan Tingkat Adversity Quotient Siswa. Majamath: Jurnal Matematika Dan Pendidikan Matematika, 5(1), 61–71. https://doi.org/10.36815/majamath.v5i1.1778
Putri, S. A., Ningsih, Y. L., & Marhamah. (2023). Kemampuan Representasi Matematis Siswa dengan Pendekatan Pemodelan Matematika pada Materi Eksponen. Laplace : Jurnal Pendidikan Matematika, 6(2), 413–420. https://doi.org/10.31537/laplace.v6i2.1455
Rahma, A. F. (2022). Analisis Kesalahan Siswa SMA dalam Menyelesaikan Soal Eksponen. Jurnal Ilmiah Pendidikan Matematika, 11(2), 446–457. https://doi.org/10.26740/mathedunesa.v11n2.p446-457
Ramdhani, S. (2018). Kemampuan Generalisasi Mahasiswa pada Perkuliahan Kapita Selekta Matematika SMA. Jurnal Analisa, 4(2), 83–89. https://doi.org/10.15575/ja.v4i2.3926
Rehman, N., Huang, X., Mahmood, A., AlGerafi, M. A. M., & Javed, S. (2024). Project-based learning as a catalyst for 21st-Century skills and student engagement in the math classroom. Heliyon, 10(23). https://doi.org/10.1016/j.heliyon.2024.e39988
Rezki, R., Suharna, H., & Sari, D. P. (2023). Analisis Kesalahan Siswa dalam Menyelesaikan Soal pada Materi Eksponensial. Jurnal Pendidikan Guru Matematika, 3(1), 23–33. https://doi.org/10.33387/jpgm.v3i1.5734
Saputri, R., Warti, R., & Murtadlo, A. (2023). Pengaruh Model Pembelajaran Pace Terhadap Kemampuan Berpikir Kreatif Matematis. Matheduca: Jurnal Matematika Dan Pendidikan Matematika, 2(7), 96–110.
Setiawan, Y. E., Purwanto, Parta, I. N., & Sisworo. (2020). Generalization strategy of linear patterns from field-dependent cognitive style. Journal on Mathematics Education, 11(1), 77–94. https://doi.org/10.22342/jme.11.1.9134.77-94
Siregar, N. (2019). Upaya Meningkatkan Kemampuan Penalaran dan Komunikasi Matematis Siswa Melalui Model PACE. Pedagogy : Jurnal Pendidikan Matematika, 4(2), 58–70. https://doi.org/10.30605/pedagogy.v4i2.1443
Sitorus, Y. I., & Sutirna. (2023). Analisis Kemampuan Generalisasi Siswa SMP Negeri 08 Karawang pada Materi Segitiga. Jurnal Ilmiah Pendidikan Matematika, 6(1), 60–75. https://doi.org/10.26877/jipmat.v6i1.8019
Solihah, R. N., & Selawati, S. (2024). Pengembangan Modul Ajar Terpadu dengan Model Berbasis Masalah Tema Ragam Bentang dan Profesi di Kelas 4 Sekolah Dasar. Jurnal Penelitian Pendidikan, 24(2), 180–190. https://doi.org/10.17509/jpp.v24i2.73344
Suryowati, E., & Aini, N. (2025). Development of Functional Thinking-Based Student Worksheets to Improve Mathematical Generalization Abilities. Jurnal Pendidikan MIPA, 26(3), 1549–1564. https://doi.org/10.23960/jpmipa.v26i3.pp1549-1564
Suwanto, F. R., Wijaya, A., Aprisal, Fauzi, A., & Tobondo, Y. V. (2023). Realistic Mathematics Textbook Toward The Students’ Mathematical Generalization Skills. Mosharafa: Jurnal Pendidikan Matematika, 12(2), 291–300. https://doi.org/10.31980/mosharafa.v12i2.2617
Tampubolon, A., Hutagalung, C. F., & Kembaren, S. N. B. (2025). Analisis Kemampuan Berpikir Komputasional Matematis Siswa Sma Pada Materi Fungsi. Pedagogy: Jurnal Pendidikan Matematika, 10(4), 2432–2450. https://doi.org/10.30605/pedagogy.v10i4.7713
Varhol, A., Drageset, O. G., & Hansen, M. N. (2021). Discovering key interactions. How student interactions relate to progress in mathematical generalization. Mathematics Education Research Journal, 33(2), 365–382. https://doi.org/10.1007/s13394-020-00308-z
Wahyuni, D., Anwar, Y. A. S., & Purwoko, A. A. (2022). Analisis Kemampuan Berpikir Logis Siswa Kelas XI MIPA SMA Negeri di Praya Selama Pembelajaran Daring. Chemistry Education Practice, 5(1), 10–16. https://doi.org/10.29303/cep.v5i1.2788
Wilkie, K. J. (2016). Students’ use of variables and multiple representations in generalizing functional relationships prior to secondary school. Educational Studies in Mathematics, 93(3), 333–361. https://doi.org/10.1007/s10649-016-9703-x
Yasmin, Y., & Negara, H. R. P. (2024). Pengaruh Model Pembelajaran Problem Based Learning Terhadap Kemampuan Computational Thinking ditinjau dari Self-Confidence Siswa. Kognitif: Jurnal Riset HOTS Pendidikan Matematika, 4(2), 885–896. https://doi.org/10.51574/kognitif.v4i2.2089
Yuni, Y., & Fisa, L. (2020). Pembelajaran Penemuan Terbimbing terhadap Kemampuan Generalisasi Matematis Siswa Sekolah Menengah Pertama. Journal of Instructional Mathematics, 1(1), 20–30. https://doi.org/10.37640/jim.v1i1.267
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Riski Novalina, Yusuf Hartono
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
