Guided Discovery Learning Integrated with Numbered Heads Together: Effects on Mathematical Problem-Solving and Student Engagement
), Nidya Ferry Wulandari(2)
| 
Country:
(1) Department of Mathematics Education, Universitas Islam Negeri Sunan Kalijaga, Indonesia
(2) Department of Mathematics Education, Universitas Islam Negeri Sunan Kalijaga, Indonesia
Corresponding Author
This study aims to determine the effectiveness of the Guided Discovery Learning (GDL) model integrated with the Numbered Heads Together (NHT) cooperative approach in improving students’ mathematical problem-solving ability and student engagement. Effectiveness in this research is operationally defined as a statistically and practically significant improvement in students’ scores and engagement compared to conventional learning. This research employed a quasi-experimental design with a nonequivalent control group. The participants were three intact eighth-grade classes at SMPN 1 Jetis Bantul, selected via cluster random sampling. Class VIII A was taught using GDL combined with NHT, class VIII D used GDL without group work, and class VIII B used conventional learning. Data were collected through a mathematical problem-solving test and a student engagement scale, both validated by experts and tested for reliability. Data analysis used One-Way ANOVA followed by a Tukey HSD post hoc test and Kruskal–Wallis to determine significant mean differences among the three groups, complemented by effect size interpretation to assess the magnitude of differences. The results revealed that the GDL with the NHT model was significantly more effective than conventional learning in improving students’ mathematical problem-solving ability (p < 0.05, Cohen’s d = 0.86). However, there was no statistically significant difference between the GDL+NHT and GDL-only groups, indicating that adding NHT did not confer a significant cognitive benefit beyond the GDL model alone. In contrast, the NHT component meaningfully enhanced students’ engagement, particularly in participatory aspects such as oral, visual, and motor engagement, compared to both the GDL-only and conventional groups. The GDL model, either with or without NHT, effectively enhances students’ mathematical problem-solving ability and student engagement compared to conventional instruction. Future studies are recommended to examine this integration in broader contexts and longer durations to explore its potential for sustainable classroom engagement.
Keywords: effectiveness, problem-solving ability, student engagement, guided discovery learning model with numbered heads together, quasi-experimental design.
Alhazmi, A., & Nyeem, H. (2022). Enhancing students’ engagement through cooperative discovery learning in mathematics classrooms. International Journal of Instruction, 15(4), 1–18. https://doi.org/10.29333/iji.2022.1541a
Anggrayni, D., Haryanto, & Syaiful. (2021). Analisis epistemic cognition siswa dalam pemecahan masalah matematika ditinjau dari gaya kognitif materi teori peluang [Analysis of students’ epistemic cognition in solving mathematical problems as viewed from the cognitive style of probability theory]. Jurnal Cendekia: Jurnal Pendidikan Matematika, 5(1), 829–841. https://doi.org/10.31004/cendekia.v5i1.557
Aprilia, R., Nursit, I., & Ilmi, Y. I. N. (2024). Efektivitas model pembelajaran Guided Discovery Learning berbantuan media Liveworksheet terhadap pemecahan masalah matematis siswa kelas VIII materi relasi dan fungsi [The effectiveness of the guided discovery learning model assisted by liveworksheet media on eighth-grade students’ mathematical problem solving on relations and functions]. Jurnal Penelitian, Pendidikan, dan Pembelajaran, 19(9), 1–11.
Astutik, P., & Wulandari, S. S. (2020). Analisis model pembelajaran Number Head Together dalam meningkatkan keaktifan siswa [Analysis of the number head together learning model in increasing student activity]. Jurnal Pendidikan Administrasi Perkantoran (JPAP), 9(1), 154–168. https://doi.org/10.26740/jpap.v9n1.p154-168
Churniawan, D., Nafiah, & Amin, S. M. (2020). Peningkatan hasil belajar melalui penerapan metode Guided Discovery Learning pada siswa kelas VI SD Negeri Kolomayan 01 Blitar [Improving learning outcomes through the application of the Guided Discovery Learning method in sixth-grade students at SDN Kolomayan 01 Blitar]. Prosiding National Conference for Ummah, 1(1), 508–523.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
Daulay, I. S., Harahap, R. A. S., & Harahap, D. (2023). Pengaruh model pembelajaran numbered heads together terhadap keaktifan belajar siswa [The effect of the numbered heads together learning model on student learning activity]. Indo-MathEdu Intellectuals Journal, 4(2), 1382–1391. https://doi.org/10.54373/imeij.v4i2.364
Eismawati, E., Koeswanti, H. D., & Radia, E. H. (2019). Peningkatan hasil belajar matematika melalui model pembelajaran Problem Based Learning (PBL) siswa kelas 4 SD [Improving mathematics learning outcomes through the Problem-Based Learning (PBL) model for fourth-grade elementary students]. Jurnal Mercumatika: Jurnal Penelitian Matematika dan Pendidikan Matematika, 3(2), 71–78. https://doi.org/10.26486/jm.v3i2.694
Erfan, M., Sari, N., Suarni, N., Maulyda, M. A., & Indraswati, D. (2020). Peningkatan hasil belajar kognitif melalui model pembelajaran kooperatif tipe Numbered Head Together (NHT) tema perkalian dan pembagian pecahan [Improving cognitive learning outcomes through the Numbered Heads Together (NHT) cooperative learning model on the theme of multiplication and division of fractions]. Jurnal IKA PGSD UNARS, 8(1), 108–118. https://doi.org/10.36841/pgsdunars.v8i1.588
Fathoni, A. Y. (2022). Upaya peningkatan keaktifan peserta didik kelas VIII A SMP Muhammadiyah 1 Godean menggunakan model guided discovery learning [Efforts to increase the activity of grade VIII A students at SMP Muhammadiyah 1 Godean using the guided discovery learning model]. Postulat: Jurnal Inovasi Pendidikan Matematika, 2(2), 133–141. https://doi.org/10.30587/postulat.v2i2.2650
Gillies, R. M. (2016). Cooperative learning: Review of research and practice. Australian Journal of Teacher Education, 41(3), 39–54. https://doi.org/10.14221/ajte.2016v41n3.3
Hosnan, M. (2014). Pendekatan saintifik dan kontekstual dalam pembelajaran abad 21: Kunci sukses implementasi kurikulum 2013 [Scientific and contextual approaches in 21st century learning: The key to successful implementation of the 2013 curriculum]. Ghalia Indonesia.
Hwang, G. J., & Chen, P. Y. (2021). Effects of a collaborative discovery learning approach on students’ higher-order thinking and motivation. Computers & Education, 168, 104219. https://doi.org/10.1016/j.compedu.2021.104219
Indriati, N. M., & Siagian, P. (2024). Pengembangan LKPD berbasis guided discovery learning berbantuan Geogebra untuk meningkatkan kemampuan pemecahan masalah kelas XI [Development of Guided Discovery Learning-based LKPD assisted by Geogebra to improve problem-solving skills in grade XI]. Koordinat Jurnal MIPA, 5(1), 1–11. https://doi.org/10.24239/koordinat.v5i1.88
Irwana, A., Surahmat, & Fuady, A. (2023). Peningkatan kemampuan pemecahan masalah matematis menggunakan model pembelajaran kooperatif tipe PDEODE materi peluang siswa kelas VIII MTs Diponegoro Tumpang [Improving mathematical problem-solving skills using the PDEODE cooperative learning model on probability material among grade VIII students of MTs Diponegoro Tumpang]. Jurnal Penelitian, Pendidikan, dan Pembelajaran, 18(26), 1–7.
Janah, S. R., Khikmiyah, F., & Astari, N. C. (2024). Upaya peningkatan keaktifan belajar peserta didik melalui model pembelajaran guided discovery learning pokok bahasan statistika pada kelas X-C SMAN 3 Tuban [Efforts to improve student learning engagement through the guided discovery learning model on statistics in class X-C of SMAN 3 Tuban]. Proceeding International Conference on Lesson Study, 1(1), 420. https://doi.org/10.30587/icls.v1i1.7193
Kanza, N. R. F., Lesmono, A. D., & Widodo, H. M. (2020). Analisis keaktifan belajar siswa menggunakan model project based learning dengan pendekatan STEM pada pembelajaran fisika materi elastisitas di kelas XI MIPA 5 SMA Negeri 2 Jember [Analysis of students’ learning activity using the project-based learning model with a STEM approach in physics learning on elasticity]. Jurnal Pembelajaran Fisika, 9(2), 71–77. https://doi.org/10.19184/jpf.v9i1.17955
Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41(2), 75–86. https://doi.org/10.1207/s15326985ep4102_1
Kurniawan, R., Nur, L., & Sari, A. (2020). Implementasi numbered heads Together dalam meningkatkan aktivitas dan hasil belajar matematika siswa SMP [Implementation of the numbered heads together model to improve students’ activity and mathematics achievement in junior high school]. Jurnal Pendidikan Matematika, 14(2), 102–113. https://doi.org/10.21831/jpm.v14i2.36592
Lafuente-Lechuga, M., Cifuentes-Faura, J., & Faura-Martínez, Ú. (2020). Mathematics applied to the economy and sustainable development goals: A necessary relationship of dependence. Education Sciences, 10(11), 1–12. https://doi.org/10.3390/educsci10110339
Laila, Z., Aima, Z., & Yunita, A. (2021). Analisis kemampuan pemecahan masalah matematis ditinjau dari minat belajar siswa [Analysis of mathematical problem-solving ability based on students’ learning interest]. Horizon, 1(3), 588–600. https://doi.org/10.22202/horizon.v1i3.5257
Langi’, E. L., Ba’ru, Y., & Paluta, E. T. (2023). Efektivitas model pembelajaran guided discovery learning terhadap kemampuan pemecahan masalah matematika siswa kelas VII SMP Negeri 3 Buntao’ Satap [Effectiveness of the guided discovery learning model on mathematical problem-solving skills of seventh-grade students at SMP Negeri 3 Buntao’ Satap]. Prosiding Seminar Nasional Pendidikan Matematika Universitas Kristen Indonesia Toraja, 2(4), 51–57.
Maharani, D., & Kusumah, Y. S. (2022). Guided discovery learning to develop mathematical reasoning and representation abilities. International Journal of Emerging Mathematics Education, 6(1), 11–21. https://doi.org/10.12928/ijeme.v6i1.22901
Manurung, P. S., Simamora, E., & Surya, E. (2022). Peningkatan kemampuan pemecahan masalah dan kemandirian belajar matematis siswa melalui model pembelajaran berbasis masalah di SMP Negeri 2 Tanjung Balai [Improving students’ problem-solving skills and mathematical learning independence through problem-based learning at SMP Negeri 2 Tanjung Balai]. Jurnal Cendekia: Jurnal Pendidikan Matematika, 6(2), 2352–2366.
Markaban. (2008). Model penemuan terbimbing pada pembelajaran matematika SMK [Guided discovery model in vocational school mathematics learning]. Pusat Pengembangan dan Pemberdayaan Pendidik dan Tenaga Kependidikan Matematika.
Maryani, Matsum, J. H., & Witarsa. (2018). Studi komparasi model pembelajaran Guided Discovery Learning dan Team Assisted Individualization di MA [Comparative study of the Guided Discovery Learning and Team Assisted Individualization learning models in Islamic senior high schools]. Jurnal Pendidikan dan Pembelajaran Khatulistiwa, 8(10), 1–9.
Maulida, R. R., & Trimurtini. (2024). Penerapan teknologi Wordwall dalam pembelajaran di sekolah dasar untuk mewujudkan tujuan keempat SDGs [The application of Wordwall technology in elementary school learning to achieve the fourth SDG goal]. Jurnal Penelitian Pendidikan Indonesia, 1(3), 372–377.
Mutiah, S., Rohman, N., & Hasanudin, C. (2023). Analisis kemampuan pemecahan masalah matematis siswa kelas VIII MTs Darul Falah Terpadu pada materi peluang ditinjau dari gender [Analysis of mathematical problem-solving ability of grade VIII students of MTs Darul Falah Terpadu on probability material by gender]. Jurnal Edumatic: Jurnal Pendidikan Matematika, 4(2), 7–17. https://doi.org/10.21137/edumatic.v4i2.789
Mutmainnah, I. W. (2020). Pengaruh guided discovery learning terhadap kemampuan pemecahan masalah matematika siswa kelas IV sekolah dasar [The effect of guided discovery learning on mathematical problem-solving ability of fourth-grade elementary school students]. Jurnal Pendidikan Guru Sekolah Dasar, 1–17.
OECD. (2023). PISA 2022 results (Volume I): The state of learning and equity in education. OECD Publishing. https://doi.org/10.1787/53f23881-en
Pranoto, Harlita, & Santosa, S. (2017). Perbandingan model pembelajaran Problem Based Learning dan Guided Discovery Learning terhadap keaktifan siswa kelas X SMA [Comparison of the Problem-Based Learning and Guided Discovery Learning models on tenth-grade students’ learning activity]. Bioedukasi, 10(1), 18–22.
Prasetyowati, D., Rasiman, & Kartinah. (2022). The effect of video-assisted discovery learning model on junior high school students’ mathematical communication. KnE Social Sciences, 204–212. https://doi.org/10.18502/kss.v7i14.11969
Pratiwi, A. N., Azizah, M., & Kartinah. (2023). Efektivitas model guided discovery learning terhadap kemampuan pemecahan masalah materi bangun ruang kelas V [Effectiveness of the guided discovery learning model on problem-solving ability of fifth-grade students in spatial construction material]. Jurnal Kualita Pendidikan, 4(1), 60–65. https://doi.org/10.51651/jkp.v4i1.345
Putra, A. H. S. (2015). Pengaruh pembelajaran penemuan terbimbing terhadap keaktifan siswa dan prestasi belajar matematika siswa kelas VIII SMP [The effect of Guided Discovery Learning on student engagement and mathematics achievement in grade VIII junior high school]. Jurnal Ilmiah Edukasi Matematika (JIEM), 1(2), 235–255.
Putri, A., Afifah, N. G., Sriyanti, A., Suharti, & Munirah. (2024). Analisis kemampuan pemecahan masalah matematis siswa pada materi peluang ditinjau dari minat belajar siswa [Analysis of students’ mathematical problem-solving ability in probability material viewed from learning interest]. Al Asma: Journal of Islamic Education, 6(1), 88–97. https://doi.org/10.24252/asma.v6i1.46728
Putri, T. R. (2025). Pengaruh model pembelajaran discovery learning terhadap kemampuan pemecahan masalah matematis dan resiliensi matematis siswa [The effect of the discovery learning model on students’ mathematical problem-solving ability and mathematical resilience]. Universitas Islam Negeri Syarif Hidayatullah.
Rahayu, W., Wibowo, T., & Purwoko, R. Y. (2018). Pengaruh model NHT terhadap kemampuan pemecahan masalah dan kerjasama belajar pada siswa SMP [The effect of the NHT model on problem-solving ability and learning cooperation among junior high school students]. Jurnal Ekuivalen, 33(1), 65–70.
Rahman, M. A., Rosli, R., & Saleh, Z. (2021). The effect of guided discovery learning on students’ mathematical problem-solving ability. European Journal of Educational Research, 10(3), 1121–1132. https://doi.org/10.12973/eu-jer.10.3.1121
Riansyah, M., Hardianti, D., & Asyhara, S. A. (2023). The effect of numbered heads together learning model on students’ mathematical problem-solving ability. Hipotenusa Journal of Research Mathematics Education (HJRME), 6(1), 73–81. https://doi.org/10.36269/hjrme.v6i1.1427
Rini, A. P., Sa’diyah, I. K., & Muhid, A. (2021). Model pembelajaran guided discovery learning, apakah efektif dalam meningkatkan kemampuan berpikir kritis siswa? [Guided discovery learning model: Is it effective in improving students’ critical thinking skills?]. Edukatif: Jurnal Ilmu Pendidikan, 3(5), 2419–2429. https://doi.org/10.31004/edukatif.v3i5.641
Rumana, K. Y. (2019). Efektivitas pembelajaran matematika menggunakan model guided discovery dilengkapi dengan metode Make A Match terhadap pemahaman konsep dan keaktifan siswa SMP kelas VIII [Effectiveness of mathematics learning using the guided discovery model combined with the Make A Match method on concept understanding and student activeness]. Universitas Islam Negeri Sunan Kalijaga.
Silitonga, H. R. (2024). Efektivitas model pembelajaran kooperatif tipe numbered head together terhadap kemampuan pemecahan masalah matematis siswa kelas VII SMP Negeri 16 Medan [Effectiveness of the numbered head Together cooperative learning model on mathematical problem-solving ability of seventh-grade students at SMP Negeri 16 Medan]. Journal of Student Research, 2(2), 56–66. https://doi.org/10.55606/jsr.v2i2.2777
Siswanto, E., & Meiliasari, M. (2024). Kemampuan pemecahan masalah pada pembelajaran matematika: Systematic literature review [Problem-solving ability in mathematics learning: A systematic literature review]. Jurnal Riset Pembelajaran Matematika Sekolah, 8(1), 45–59. https://doi.org/10.21009/jrpms.081.06
Slavin, R. E. (2019). Educational psychology: Theory and practice (13th ed.). Pearson Education.
Sriwahyuni, K., & Maryati, I. (2022). Kemampuan pemecahan masalah matematis siswa pada materi statistika [Students’ mathematical problem-solving ability on statistics material]. Plusminus: Jurnal Pendidikan Matematika, 2(2), 335–344. https://doi.org/10.31980/plusminus.v2i2.1830
Sugiyono. (2019). Metode penelitian pendidikan [Educational research methods] (3rd ed.). Alfabeta.
Sunita, N. W., Erawati, N. K., Parmithi, N. N., & Purnamawati, N. P. W. (2021). Pengaruh model pembelajaran kooperatif tipe numbered head together terhadap kemampuan pemecahan masalah matematis dengan mengontrol kecerdasan emosional [The effect of the numbered heads together cooperative learning model on mathematical problem-solving ability while controlling emotional intelligence. Mosharafa: Jurnal Pendidikan Matematika, 10(1), 68–78.
Talelu, D., Mamoh, O., & Klau, K. Y. (2022). Pengaruh kedisiplinan belajar dan keaktifan belajar siswa terhadap prestasi belajar matematika siswa kelas VIII SMP Negeri Fatumfaun [The effect of learning discipline and student activeness on mathematics learning achievement of eighth-grade students at SMP Negeri Fatumfaun]. Numeracy, 9(1), 39–51. https://doi.org/10.46244/numeracy.v9i1.1741
Tasliah, A. L., Nuraeni, A., & Fauzi, R. I. (2024). Literasi digital: Kunci menuju pendidikan berkualitas melalui perspektif SDGs 2030 [Digital literacy: The key to quality education through the SDGs 2030 perspective]. Jurnal Multidisiplin Ilmu Akademik, 1(3), 154–165.
Varod, V. S., Alkalai, Y. E., & Geri, N. (2019). Tracing research trends of 21st-century learning skills. British Journal of Educational Technology, 50(6), 1–20. https://doi.org/10.1111/bjet.12753
Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Harvard University Press.
Refbacks
- There are currently no refbacks.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.