Teaching of Mathematical Proof in Middle School Geometry: A Systematic Review of Technology-Enhanced Approaches
DOI:
https://doi.org/10.18326/hipotenusa.v8i1.6433Kata Kunci:
mathematical proof, middle school, technology integration, dynamic geometry software, systematic literature reviewAbstrak
This study investigates approaches to teaching mathematical proof at the middle school level through a systematic literature review, focusing on a key challenge in mathematics education: the difficulty students face in transitioning from empirical to deductive reasoning. Mathematical proof is a foundational element of mathematical reasoning, yet many students struggle with this shift. This study synthesizes empirical research on instructional approaches, particularly those that integrate technology, such as dynamic geometry software, augmented reality (AR), and digital learning tools, to improve students' proof skills. Following the PRISMA 2020 protocol, a systematic review was conducted with searches in Scopus, Web of Science, ERIC, and Google Scholar for studies published between 2014 and 2025. Forty-two empirical studies met the inclusion criteria. The findings highlight that technology-enhanced approaches, especially the use of dynamic geometry software, significantly improve students' abilities in proof construction, validation, and reasoning compared to conventional methods. Furthermore, the study identifies common challenges faced by teachers, including limited pedagogical content knowledge and difficulties in guiding students through the transition to formal proof. The review underscores the need to integrate inquiry-based learning and technology tools to foster deeper understanding of proofs at the middle school level. The study’s contribution lies in synthesizing diverse instructional strategies and providing evidence-based insights for future educational practices. Implications for practice and future research are also discussed.
Referensi
Agoestanto, A., & Rinachyuan, W. (2020). Student error analysis in global meta-level algebraic thinking on treffinger learning assisted by scaffolding. Journal of Physics: Conference Series, 1567(2), 022092. https://doi.org/10.1088/1742-6596/1567/2/022092
Anwar, L., Goedhart, M. J., & Mali, A. (2023). Learning trajectory of geometry proof construction: Studying the emerging understanding of the structure of Euclidean proof. Eurasia Journal of Mathematics, Science and Technology Education, 19(5), em2266. https://doi.org/10.29333/ejmste/13160
Aprilianty, D. R., Meryansumayeka, M., Scristia, S., & Yusuf, M. (2024). Kemampuan Pembuktian Matematika Siswa Sma Pada Materi Trigonometri Menggunakan Pembelajaran Berbasis Bukti Berbantuan Software Geogebra. SJME (Supremum Journal of Mathematics Education), 8(2), 153–171. https://doi.org/10.35706/sjme.v8i2.11095
Arisoy, B., & Aybek, B. (2021). The Effects of Subject-Based Critical Thinking Education in Mathematics on Students’ Critical Thinking Skills and Virtues. Eurasian Journal of Educational Research, 21(92). https://doi.org/10.14689/ejer.2021.92.6
Bilad, M. R., Zubaidah, S., & Prayogi, S. (2024). Addressing the PISA 2022 Results: A Call for Reinvigorating Indonesia’s Education System. International Journal of Essential Competencies in Education, 3(1), 1–12. https://doi.org/10.36312/ijece.v3i1.1935
Blair, K. (2021). On the Appropriateness and Necessity of Proofs and Proving in Middle School Mathematics Classrooms. 10(1), 1–10.
Cheah, U. H. (2018). Designing Instruction in Geometry: Using Lesson Study to Improve Classroom Teaching (pp. 181–195). https://doi.org/10.1007/978-3-319-77476-3_11
Chen, J., & Jin, S. (2025). Research on Teaching Design for Cultivating Middle School Students’ Geometric Intuitive Ability Based on Virtual Reality Technology. International Journal of New Developments in Education, 7(4). https://doi.org/10.25236/IJNDE.2025.070406
Chen, J., Zhou, Y., Wijaya, T. T., & Tamur, M. (2021). Is a triangle 180 degrees? Using relevant material to explore elementary school students’ reasoning ability. International Journal of Education and Learning, 3(3), 199–212. https://doi.org/10.31763/ijele.v3i3.295
Dahal, N., Pant, B. ., Shrestha, I. ., & Manandhar, N. . (2022). Use of GeoGebra in Teaching and Learning Geometric Transformation in School Mathematics. International Journal of Interactive Mobile Technologies (IJIM), 16(08), 65–78. https://doi.org/10.3991/ijim.v16i08.29575
Darmawijoyo, D., Zulkardi, Z., Putri, R. I. I., Hapizah, H., & Syutaridho, S. (2025). How do students use mathematical reasoning to solve PISA-type mathematics problems based on making kite contexts? Infinity Journal, 14(4), 1065–1080. https://doi.org/10.22460/infinity.v14i4.p1065-1080
Elisyah, N., Fonna, M., & Ayunda, D. S. (2024). Praktikalitas Media Pembelajaran Matematika pada Materi Aljabar Berbasis Pendekatan PMRI. Indo-MathEdu Intellectuals Journal, 5(3), 3434–3440. https://doi.org/10.54373/imeij.v5i3.1142
Fujita, T., & Jones, K. (2014). Reasoning-and-proving in geometry in school mathematics textbooks in Japan. International Journal of Educational Research, 64, 81–91. https://doi.org/10.1016/j.ijer.2013.09.014
Fukaya, T., Nakamura, D., Kitayama, Y., & Nakagoshi, T. (2025). A systematic review and meta-analysis of research on mathematics and science pedagogical content knowledge: Exploring its associations with teacher and student variables. Teaching and Teacher Education, 155, 104881. https://doi.org/10.1016/j.tate.2024.104881
Güler, G. (2016). The Difficulties Experienced in Teaching Proof to Prospective Mathematics Teachers: Academician Views. Higher Education Studies, 6(1), 145. https://doi.org/10.5539/hes.v6n1p145
Haj-Yahya, A. (2022). Students’ conceptions of the definitions of congruent and similar triangles. International Journal of Mathematical Education in Science and Technology, 53(10), 2703–2727. https://doi.org/10.1080/0020739X.2021.1902008
Hartono, S. (2025). Evolving trends in mathematical proof research in Indonesian mathematics education: A systematic review from design to data analysis. Multidisciplinary Reviews, 8(12), 2025372. https://doi.org/10.31893/multirev.2025372
Hollebrands, K., & Ozen, D. (2020). Prospective high school mathematics teachers’ uses of diagrams and geometric transformations while reasoning about geometric proof tasks. Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 676–680. https://doi.org/10.51272/pmena.42.2020-99
Hong, Q. N., Fàbregues, S., Bartlett, G., Boardman, F., Cargo, M., Dagenais, P., Gagnon, M., Griffiths, F., Nicolau, B., O’Cathain, A., Rousseau, M., Vedel, I., & Pluye, P. (2018). The Mixed Methods Appraisal Tool (MMAT) version 2018 for information professionals and researchers. Education for Information, 34(4), 285–291. https://doi.org/10.3233/EFI-180221
Hsu, H., & Silver, E. . (2026). Cognitive complexity of geometric proof and geometric calculation: a problem-solving perspective. Educational Studies in Mathematics, 121(1), 29–50. https://doi.org/10.1007/s10649-025-10434-9
Hu, N., & Yin, L. (2025). Research on Cultivating Geometric Intuitive Literacy of Junior High School Students Based on Graphic Movement and Splicing (pp. 194–201). https://doi.org/10.2991/978-2-38476-440-2_23
Hu, Y., & Zhang, Y. (2025). A Study on Instructional Design for Geometry Reasoning Ability Based on Van Hiele Theory. Curriculum and Teaching Methodology, 8(7). https://doi.org/10.23977/curtm.2025.080718
İbili, E., Çat, M., Resnyansky, D., Şahin, S., & Billinghurst, M. (2020). An assessment of geometry teaching supported with augmented reality teaching materials to enhance students’ 3D geometry thinking skills. International Journal of Mathematical Education in Science and Technology, 51(2), 224–246. https://doi.org/10.1080/0020739X.2019.1583382
Jamaan, E. Z., & Yerizon, Y. (2023). Enhancing teacher creativity in digitalizing math-literacy modules through technological pedagogical content knowledge training. Al-Jabar : Jurnal Pendidikan Matematika, 14(1), 141–151. https://doi.org/10.24042/ajpm.v14i1.16832
Karpuz, Y., & Güven, B. (2022). Are 9th Grade Students Ready to Engage in the Theoretical Discursive Process in Geometry? Journal of Research in Mathematics Education, 11(1), 86–112. https://doi.org/10.17583/redimat.3667
Komatsu, K., & Jones, K. (2022). Generating mathematical knowledge in the classroom through proof, refutation, and abductive reasoning. Educational Studies in Mathematics, 109(3), 567–591. https://doi.org/10.1007/s10649-021-10086-5
Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4, 1–12. https://doi.org/10.3389/fpsyg.2013.00863
Lessing, M., & Ogbonnaya, U. (2025). Reasoning and proof in mathematics education: a systematic literature review. Discover Education, 5. https://doi.org/10.1007/s44217-025-01016-1
Levin, M., & Walkoe, J. (2022). Seeds of algebraic thinking: a Knowledge in Pieces perspective on the development of algebraic thinking. ZDM – Mathematics Education, 54(6), 1303–1314. https://doi.org/10.1007/s11858-022-01374-2
Machisi, E., & Feza, N. N. (2021). Van Hiele Theory-Based Instruction and Grade 11 Students’ Geometric Proof Competencies. Contemporary Mathematics and Science Education, 2(1), 1–6. https://doi.org/10.30935/conmaths/9682
Marian, F., Efendi, D., & Abdillah, K. M. (2025). Integrasi teknologi augmented reality dalam pembelajaran matematika untuk meningkatkan pemahaman geometri siswa. JIPMat, 10(2), 255–270. https://doi.org/10.26877/jipmat.v10i2.2510
Mavani, D., Mavani, B., & Schäfer, M. (2018). A Case Study of Two Selected Teachers as they Integrated Dynamic Geometry Software as a Visualisation Tool in Teaching Geometry. African Journal of Research in Mathematics, Science and Technology Education, 22(3), 297–307. https://doi.org/10.1080/18117295.2018.1522716
Miyazaki, M., Fujita, T., Iwata, K., & Jones, K. (2024). Level-spanning proof-production strategies to enhance students’ understanding of the proof structure in school mathematics. International Journal of Mathematical Education in Science and Technology, 55(7), 1597–1618. https://doi.org/10.1080/0020739X.2022.2075288
Naufal, M. A., Abdullah, A. H., Osman, S., Abu, M. S., Ihsan, H., & Rondiyah, R. (2021). Reviewing the Van Hiele model and the application of metacognition on geometric thinking. International Journal of Evaluation and Research in Education (IJERE), 10(2), 597. https://doi.org/10.11591/ijere.v10i2.21185
Obara, S., & Nie, B. (2023). Mathematics Teachers’ Geometric Thinking: A Case Study of In-service Teachers’ Constructing, Conjecturing, and Exploring with Dynamic Geometry Software. European Journal of Mathematics and Science Education, volume-4-2(volume-4-issue-1-march-2023), 65–78. https://doi.org/10.12973/ejmse.4.1.65
Page, M. J., McKenzie, J. E., Bossuyt, P. M., Boutron, I., Hoffmann, T. C., Mulrow, C. D., Shamseer, L., Tetzlaff, J. M., Akl, E. A., Brennan, S. E., Chou, R., Glanville, J., Grimshaw, J. M., Hróbjartsson, A., Lalu, M. M., Li, T., Loder, E. W., Mayo-Wilson, E., McDonald, S., … Moher, D. (2021). The PRISMA 2020 statement: an updated guideline for reporting systematic reviews. BMJ, n71. https://doi.org/10.1136/bmj.n71
Puspa, E. (2015). Pengembangan soal matematika model pisa untuk mengetahui argumentasi siswa di Sekolah Menengah Pertama. Jurnal Pendidikan Matematika, 9(2), 124–147.
Putra, Z. H., Afrillia, Y. M., Dahnilsyah, & Tjoe, H. (2023). Prospective elementary teachers’ informal mathematical proof using GeoGebra: The case of 3D shapes. Journal on Mathematics Education, 14(3), 449–468. https://doi.org/10.22342/jme.v14i3.pp449-468
Ramírez-Uclés, R., & Ruiz-Hidalgo, J. F. (2022). Reasoning, Representing, and Generalizing in Geometric Proof Problems among 8th Grade Talented Students. Mathematics, 10(5), 789. https://doi.org/10.3390/math10050789
Rocha, H. (2019). Mathematical proof: From mathematics to school mathematics. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 377(2140). https://doi.org/10.1098/rsta.2018.0045
Santos-Trigo, M. (2024). Problem solving in mathematics education: tracing its foundations and current research-practice trends. ZDM – Mathematics Education, 56(2), 211–222. https://doi.org/10.1007/s11858-024-01578-8
Sari, Y. M., Retnawati, H., & Fiangga, S. (2022). The construct validity of mathematical reasoning and proof test instrument integrated with GeoGebra: Second-order confirmatory factor analysis. Beta: Jurnal Tadris Matematika, 15(2), 104–118. https://doi.org/10.20414/betajtm.v15i2.549
Scristia, S., Aisyah, S., Meryansumayeka, M., Safitri, E. R., & Kurniawan, H. (2022). Students’ errors in solving reasoning-based congruence proof problems. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 11(4), 3160. https://doi.org/10.24127/ajpm.v11i4.5825
Sibgatullin, I. R., Korzhuev, A. V, Khairullina, E. R., Sadykova, A. R., Baturina, R. V, & Chauzova, V. (2022). A Systematic Review on Algebraic Thinking in Education. Eurasia Journal of Mathematics, Science and Technology Education, 18(1), em2065. https://doi.org/10.29333/ejmste/11486
Sirait, A. F., Mujib, A., & Washliyah, A. (2025). Analisis Kemampuan Pembuktian Matematis Siswa SMP pada Materi Phytagoras di Tinjau dari Resiliensi dan Gaya Kognitif Siswa. Media Pendidikan Matematika, 13(1), 529–548.
Song, J., & Ge, Q. (2023). Cultivation of Mathematical Intuitive Imagination Literacy in High School Students Based on GeoGebra Software. International Journal of Innovation in Science and Mathematics, 11(5), 2347–9051, 87–92.
St. Goar, J., & Lai, Y. (2022). Designing Activities to Support Prospective High School Teachers’ Proofs of Congruence from a Transformation Perspective. PRIMUS, 32(7), 827–842. https://doi.org/10.1080/10511970.2021.1940403
Stylianides, A. J. (2016). Proving in the Elementary Mathematics Classroom. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780198723066.001.0001
Stylianides, G., Stylianides, A., & Moutsios-Rentzos, A. (2023). Proof and proving in school and university mathematics education research: a systematic review. ZDM: The International Journal on Mathematics Education, 56. https://doi.org/10.1007/s11858-023-01518-y
Sumarwati, Suryanto, E., & Ulya, C. (2025). TPACK Levels of Indonesian Language Teachers: A Survey in Rural Junior High Schools. Theory and Practice in Language Studies, 15(5), 1499–1509. https://doi.org/10.17507/tpls.1505.15
Tandililing, P., Sirampun, E., Kho, R., & Ruamba, M. Y. (2025). Geometric Thinking Levels in Learning Quadrilaterals: A Van Hiele-Based Case Study in a Papuan Junior High School. Edumatica : Jurnal Pendidikan Matematika, 15(2), 124–136. https://doi.org/10.22437/edumatica.v15i2.43719
Uyen, B. P., Tong, D. H., & Tram, N. T. B. (2021). Developing Mathematical Communication Skills for Students in Grade 8 in Teaching Congruent Triangle Topics. European Journal of Educational Research, 10(3), 1287–1302. https://doi.org/10.12973/eu-jer.10.3.1287
van Eck, N. J., & Waltman, L. (2010). Software survey: VOSviewer, a computer program for bibliometric mapping. Scientometrics, 84(2), 523–538. https://doi.org/10.1007/s11192-009-0146-3
Wang, Z., Wang, Z., & An, S. (2018). Error Analysis of 8th Graders’ Reasoning and Proof of Congruent Triangles in China. Journal of Mathematics Education, 11(2). https://doi.org/10.26711/007577152790029
Weigand, H. G., Hollebrands, K., & Maschietto, M. (2025). Geometry education at secondary level – a systematic literature review. ZDM – Mathematics Education, 57(4), 829–843. https://doi.org/10.1007/s11858-025-01703-1
Yudhi, P. (2024). Optimalisasi Lesson Study Dengan Dynamic Geometry Software (Dgs) Untuk Pengembangan Profesional Guru Matematika. Inovasi Pendidikan, 11(2), 1–8. https://www.jurnal.umsb.ac.id/index.php/inovasipendidikan/article/view/6318
Zengin, Y. (2022). Construction of proof of the Fundamental Theorem of Calculus using dynamic mathematics software in the calculus classroom. Education and Information Technologies, 27(2), 2331–2366. https://doi.org/10.1007/s10639-021-10666-1
Unduhan
Diterbitkan
Cara Mengutip
Terbitan
Bagian
Lisensi
Hak Cipta (c) 2026 As Elly, Yusuf Hartono, Nyimas Aisyah, Hapizah
Artikel ini berlisensiCreative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
