Analysis of spatial reasoning ability in solving geometric transformation problems
DOI:
https://doi.org/10.29407/jmen.v11i2.27277Keywords:
Spatial Reasoning, Geometric Transformation, Problem SolvingAbstract
Spatial reasoning ability significantly affects mathematics learning in the area of geometric transformations. However, students’ spatial reasoning ability is still underdeveloped. This study focused on analyzing students’ spatial reasoning ability while working on problems involving geometric transformations. Data were collected through a spatial reasoning ability test and personal interviews. The subjects were six grade XI students. The research design applied was descriptive qualitative. It was found that students with high spatial reasoning ability could mentally analyze and understand rotation patterns, envision objects moving in a clockwise direction, determine dilation and reflection of an object about a specific axis, and comprehend spatial changes and the position of objects and shapes in space. Students with moderate spatial reasoning ability could understand the rotation patterns and mentally picture the objects moving clockwise; however, they could not grasp the concept of object transformations correctly. Low spatial reasoning ability could not grasp the problem and visualize the rotation of the objects, resulting in an inability to determine the transformation of the object position. This also prevented the students from solving the transformation concept. This study has been able to identify specific aspects that need to be addressed in the geometric transformation topic. This research can help inform the design of more effective and innovative learning strategies.
References
Aje, C., Nuguid, M., Ünlü, M., & Ochulor, H. (2025). Spatio-Visual Reasoning and Teamwork through Hands-On STEM Construction Activities. https://doi.org/10.5703/1288284317834
Alkhateeb, M. (2018). Multiple Representations in 8th Grade Mathematics Textbook and the Extent to which Teachers Implement Them. International Electronic Journal of Mathematics Education, 14(1). https://doi.org/10.12973/IEJME/3982
Alkouri, Z. (2022). Developing spatial abilities in young children: Implications for early childhood education. Cogent Education, 9(1). https://doi.org/10.1080/2331186X.2022.2083471
Amro, D. K., & Dawoud, H. (2024). Influencing Factors of Spatial Ability for Architecture and Interior Design Students: A Fuzzy DEMATEL and Interpretive Structural Model. Buildings, 14(9). https://doi.org/10.3390/BUILDINGS14092934
Astuti, E. P. (2017). Representasi Matematis Mahasiswa Calon Guru dalam Menyelesaikan Masalah Matematika. Beta Jurnal Tadris Matematika. https://doi.org/10.20414/betajtm.v10i1.100
Astuti, E. P. (2025). Kemampuan numerasi siswa Sekolah Menengah Pertama: Sebuah studi analisis pemecahan masalah dalam konteks kehidupan nyata. Proximal: Jurnal Penelitian Matematika Dan Pendidikan Matematika, 8(2), 923–932. https://doi.org/10.30605/PROXIMAL.V8I2.6669
Astuti, E. P., Kurniasih, N., & Nugraheni, P. (2016). Pengaruh Readiness dan Self-Confidence terhadap Penguasaan Geometri Transformasi Mahasiswa Pendidikan Matematika Universitas Muhammadiyah Purworejo. https://doi.org/10.20414/betajtm.v9i1.4
Bahbah, A., Khaldi, M., & Erradi, M. (2023). Mapping of Mathematical Problem Solving Processes in Middle School Students: A Methodological and Analytical Approach. RA Journal of Applied Research, 09(02). https://doi.org/10.47191/RAJAR/V9I2.10
Battista, M. T., Frazee, L. M., & Winer, M. L. (2018). Analyzing the Relation Between Spatial and Geometric Reasoning for Elementary and Middle School Students. https://doi.org/10.1007/978-3-319-98767-5_10
Baxter, P., & Jack, S. (2008). Qualitative Case Study Methodology : Study Design and Implementation for Novice Researchers. 13, 544–559.
Bogdan, R. C., & Biklen, S. K. for Education An Introduction to Theory and Methods.
Budiarto, M. T., & Artiono, R. (2019). Geometri dan permasalahan dalam pembelajarannya (suatu penelitian meta analisis. Jurnal Magister Pendidikan Matematika (JUMADIKA, 1(1), 9–18. https://doi.org/10.30598/JUMADIKAVOL1ISS1YEAR2019PAGE9-18
Cantone, G. G., & Tomaselli, V. (2022). Hybrid Probabilistic-Snowball Sampling. https://doi.org/10.48550/ARXIV.2204.01887
Cheng, Y. L., & Mix, K. S. (2014). Spatial Training Improves Children's Mathematics Ability. Journal of Cognition and Development, 15(1), 2–11. https://doi.org/10.1080/15248372.2012.725186
Cresswell, J. W., & Cresswell, J. D. (2023). Research design: Qualitative, quantitative, and mixed methods approaches. SAGE Publications Inc.
Dahal, N., Pant, B. P., Shrestha, I. M., & Manandhar, N. K. (2022). Use of GeoGebra in Teaching and Learning Geometric Transformation in School Mathematics. International Journal of Interactive Mobile Technologies, 16(08), 65–78. https://doi.org/10.3991/IJIM.V16I08.29575
Evidiasari, S., Subanji, S., & Irawati, S. (2019). Students' Spatial Reasoning in Solving Geometrical Transformation Problems. Indonesian Journal on Learning and Advanced Education (IJOLAE, 1(2), 38–51. https://doi.org/10.23917/IJOLAE.V1I2.8703
Fujita, T., Kondo, Y., Kumakura, H., Miawaki, S., Kunimune, S., & Shojima, K. (2022). Identifying Japanese students' core spatial reasoning skills by solving 3D geometry problems: An exploration. Asian Journal for Mathematics Education, 1(4), 437–454. https://doi.org/10.1177/27527263221142345/ASSET/577C3408-B109-46F3-A6E6-FD3C0A2BC7B1/ASSETS/IMAGES/LARGE/10.1177_27527263221142345-FIG5.JPG
Harris, D. (2023). Spatial reasoning in context: bridging cognitive and educational perspectives of spatial-mathematics relations. Frontiers in Education. https://doi.org/10.3389/FEDUC.2023.1302099
Herawati, H., & Hariyani, M. (2024). Spatial thinking ability in elementary school. PIONIR: JURNAL PENDIDIKAN, 13(1). https://doi.org/10.22373/PJP.V13I1.23002
Ikhsan, M., Rochaminah, S., & Mastura, A. (2024). The Development of Geo-Math Application by Integrating Geo-Gebra Applets to Improve Students' Spatial Ability. Jurnal Ilmiah Peuradeun, 12(3), 1129–1129. https://doi.org/10.26811/PEURADEUN.V12I3.1492
Jablonski, S., & Ludwig, M. (2023). Teaching and Learning of Geometry-A Literature Review on Current Developments in Theory and Practice. Education Sciences, 13(7). https://doi.org/10.3390/EDUCSCI13070682
Juliana, A., Nurjanah, & Usdiyana, D. (2022). The learning obstacles in solving geometry problems based on spatial ability in term of Van Hiele level. Nucleation and Atmospheric Aerosols. https://doi.org/10.1063/5.0117208
Kothari, C. R., & Garg, G. (2008). Research methodology: Methods and techniques (4th ed.). New Age International Publishers. https://search.ebscohost.com/login.aspx?direct=true&db=cat08969a&AN=dut.f3ee9d93.91ec.43e7.a3b9.a1a9d6d92619&site=eds-live
Kurt, G., Önel, F., & Çakıoğlu, Ö. (2023). An investigation of Middle School Students Spatial Reasoning Skills. International Electronic Journal of Elementary Education, 16(1), 123–141. https://doi.org/10.26822/IEJEE.2023.319
Lakin, J. M., Wai, J., Olszewski-Kubilius, P., Corwith, S., Rothschild, D., & Uttal, D. H. (2024). Spatial Thinking Across the Curriculum: Fruitfully Combining Research and Practice. Gifted Child Today, 47(3), 170–177. https://doi.org/10.1177/10762175241242722
Lavicza, Z., Abar, C. A. A. P., & Tejera, M. (2023). Spatial geometric thinking and its articulation with the visualization and manipulation of objects in 3D. Educação Matemática Pesquisa, 25(2), 258–277. https://doi.org/10.23925/1983-3156.2023V25I2P258-277
Lowrie, T., & Logan, T. (2018). The Interaction Between Spatial Reasoning Constructs and Mathematics Understandings in Elementary Classrooms. https://doi.org/10.1007/978-3-319-98767-5_12
Maghfiroh, S. U., & Qothrunnada, I. (2024). Mathematical Spatial Ability and Geometry Ability: A Correlation Study. International Journal of Scientific Research and Management, 12(12), 558–566. https://doi.org/10.18535/IJSRM/V12I12.M01
Mainali, B. (2020). Representation in teaching and learning mathematics. International Journal of Education in Mathematics, Science and Technology, 9(1), 1–21. https://doi.org/10.46328/IJEMST.1111
Masamah, U., & Farabi, M. A. (2024). Students' Visual-Spatial Thinking Ability in Solving Geometry Transformation Problems Based on Jombangan Ethnomathematics in Junior High Schools. Proceeding of International Conference on Islamic Education (ICIED, 9(1), 609–609. https://doi.org/10.18860/ICIED.V9I1.3194
Mega, A. M. M. P., & Meiliasasi. (2024). Analysıs Of Students' Problem-Solvıng Abılıtıes On Hıgher Order Thınkıng Skıll (Hots) Geometry Problems In Terms Of Spatıal Reasonıng. Jurnal Elementaria Edukasia, 7(2), 2786–2800. https://doi.org/10.31949/JEE.V7I2.9574
Miles, M. B., Huberman, A. M., & Saldaña, J. (2014). Qualitative Data Analysis: A Methods Sourcebook Edition. SAGE Publication, Inc. https://books.google.co.id/books?id=p0wXBAAAQBAJ&printsec=frontcover&hl=id#v=onepage&q&f=false
N.c.t.m. (2012). Principles and Standards for School Mathematics Overview. Journal of Equine Veterinary Science.
Ningsih, S., & Hidayati, K. (2022). The role of abstraction ability in mathematical problem solving. Nucleation and Atmospheric Aerosols, 2575. https://doi.org/10.1063/5.0109166
Novita, R., Putra, M., Rosayanti, E., & Fitriati, F. (2018). Design learning in mathematics education: Engaging early childhood students in geometrical activities to enhance geometry and spatial reasoning. Journal of Physics: Conference Series, 1088(1). https://doi.org/10.1088/1742-6596/1088/1/012016
Nyimbili, F., & Nyimbili, L. (2024). Types of purposive sampling techniques with their examples and application in qualitative research studies. British Journal of Multidisciplinary and Advanced Studies, 5(1), 90–99. https://doi.org/10.37745/BJMAS.2022.0419
Popescu, A. (2021). The role of mathematical competence in the initial training of students' professional skills. Education, Society, Family. Interdisciplinary Perspectives and Analyses, 105-110. https://doi.org/10.56177/EPVL.CH14.2021.EN
Ramful, A., Lowrie, T., & Logan, T. (2017). Measurement of Spatial Ability: Construction and Validation of the Spatial Reasoning Instrument for Middle School Students. Journal of Psychoeducational Assessment, 35(7). https://doi.org/10.1177/0734282916659207;WGROUP:STRING:PUBLICATION
Rani, G., Kumar, P., Devi, R., Kumar, R., Kumar, S., & Kumar, M. (2023). Mathematics as a Part of The Real Life. International Journal of Advanced Research in Science, Communication and Technology, 3(5), 409–418. https://doi.org/10.48175/IJARSCT-11665
Riastuti, N., Mardiyana, & Pramudya, I. (2017, 2017). Analysis of students geometry skills viewed from spatial intelligence AIP Conference Proceedings, https://doi.org/10.1063/1.5016658
Rustanuarsi, R. (2023). Kemampuan spasial mahasiswa Program Studi Tadris Matematika dalam materi geometri transformasi. J-PiMat : Jurnal Pendidikan Matematika, 5(1), 705–714. https://doi.org/10.31932/J-PIMAT.V5I1.2373
Šćepanović, R. (2019). Isometric transformations in the development of spatial reasoning. Deleted Journal, 19(2), 133–154. https://doi.org/10.5937/METPRA1901133Q
Shriki, A., & Patkin, D. (2021). Developing Spatial Skills through Mental Rotation Activities. Mathematics Teacher: Learning and Teaching PK-12, 114(7), 536–544. https://doi.org/10.5951/MTLT.2020.0267
Suciati, R. A., Sobarningsih, N., Sugilar, H., Farlina, E., & Juariah. (2023). Students' error analysis in solving three dimensional problems in terms of spatial ability. Nucleation and Atmospheric Aerosols. https://doi.org/10.1063/5.0119743
Tanjung, H., Sinaga, B., & Mansyur, A. (2021). Analysis of Student's Spatial Ability in terms of Van Hiele's Thinking Stages in Problem Based Learning. Budapest International Research and Critics in Linguistics and Education (BirLE) Journal, 4(1), 470–485. https://doi.org/10.33258/BIRLE.V4I1.1675
Ulandari, L., Amry, Z., & Saragih, S. (2019). Development of Learning Materials Based on Realistic Mathematics Education Approach to Improve Students' Mathematical Problem Solving Ability and Self-Efficacy. International Electronic Journal of Mathematics Education, 14(2). https://doi.org/10.29333/IEJME/5721
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