The effectiveness of spatial integration in a mathematics learning module on students' cognitive skills: An experimental study

Rizky Oktaviana Eko Putri; Hutkemri Zulnaidi; Suzieleez Syrene Abdul Rahim; Rizky Oktaviana Eko Putri; Hutkemri Zulnaidi; Suzieleez Syrene Abdul Rahim

doi:10.3934/steme.2026007

STEM Education

2026, Volume 6, Issue 1: 140-161. doi: 10.3934/steme.2026007

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Research article Topical Sections

The effectiveness of spatial integration in a mathematics learning module on students' cognitive skills: An experimental study

Department of Mathematics and Science Education, Faculty of Education, Universiti Malaya, Kuala Lumpur, Malaysia; rizkyoktavianaputri88@gmail.com; hutkemri@um.edu.my; suzieleez@um.edu.my

Academic Editor: Zlatko Jovanoski

Received: 18 August 2025 Revised: 24 December 2025 Accepted: 27 January 2026 Published: 09 February 2026

Previous studies have demonstrated a positive relationship between spatial reasoning and cognitive skills, suggesting that spatial reasoning can forecast students' success in mathematics. This study aimed to assess the effectiveness of implementing a mathematics learning module with spatial integration on students' cognitive abilities (spatial reasoning and problem-solving), emphasizing the importance of spatial reasoning in mathematics education. This study's proposed learning module highlighted interactivity, which is absent in the current version's module. A total of 225 seventh-grade students from two public junior high schools in Indonesia volunteered for this research. The students participating in this study were divided into two groups: an experimental group and a control group, comprising 115 students in the experimental group and 110 in the control group. The experimental groups underwent mathematics learning conducted by teachers who had received spatial training and used the mathematics learning module with spatial integration, while the control groups received conventional learning. The training focused on enhancing teachers' knowledge about spatial learning in mathematics and how to use the learning module. Pre-test and post-test were conducted for both spatial reasoning and problem-solving. The gain score was considered to examine the effectiveness of the teachers' training on students' cognitive skills. The statistical analysis results indicate a significant difference between the experimental and control groups in both students' spatial reasoning and mathematics problem-solving, with the experimental group outperforming the control group. Furthermore, the implications and impacts of spatial reasoning on cognitive skills are discussed.
- spatial reasoning,
- problem-solving,
- geometry,
- spatial integration,
- learning module
Citation: Rizky Oktaviana Eko Putri, Hutkemri Zulnaidi, Suzieleez Syrene Abdul Rahim. The effectiveness of spatial integration in a mathematics learning module on students' cognitive skills: An experimental study[J]. STEM Education, 2026, 6(1): 140-161. doi: 10.3934/steme.2026007

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Abstract

Previous studies have demonstrated a positive relationship between spatial reasoning and cognitive skills, suggesting that spatial reasoning can forecast students' success in mathematics. This study aimed to assess the effectiveness of implementing a mathematics learning module with spatial integration on students' cognitive abilities (spatial reasoning and problem-solving), emphasizing the importance of spatial reasoning in mathematics education. This study's proposed learning module highlighted interactivity, which is absent in the current version's module. A total of 225 seventh-grade students from two public junior high schools in Indonesia volunteered for this research. The students participating in this study were divided into two groups: an experimental group and a control group, comprising 115 students in the experimental group and 110 in the control group. The experimental groups underwent mathematics learning conducted by teachers who had received spatial training and used the mathematics learning module with spatial integration, while the control groups received conventional learning. The training focused on enhancing teachers' knowledge about spatial learning in mathematics and how to use the learning module. Pre-test and post-test were conducted for both spatial reasoning and problem-solving. The gain score was considered to examine the effectiveness of the teachers' training on students' cognitive skills. The statistical analysis results indicate a significant difference between the experimental and control groups in both students' spatial reasoning and mathematics problem-solving, with the experimental group outperforming the control group. Furthermore, the implications and impacts of spatial reasoning on cognitive skills are discussed.

References

[1]	Nurbani, A.N. and Setiawan, R., Senior lecturers' narrative experience in traversing the transformations of curriculum: 1994 Curriculum to Merdeka curriculum. JIIP-Jurnal Ilmiah Ilmu Pendidikan, 2024, 7(1): 1105‒1116. https://doi.org/10.54371/jiip.v7i1.3893 doi: 10.54371/jiip.v7i1.3893
[2]	Hwang, G.J., Wang, S.Y. and Lai, C.L., Effects of a social regulation-based online learning framework on students' learning achievements and behaviors in mathematics. Computers & Education, 2021,160: 104031. https://doi.org/10.1016/j.compedu.2020.104031 doi: 10.1016/j.compedu.2020.104031
[3]	Smith-Peirce, R.N. and Butler, A.C., A scoping review of research on individual differences in the testing effect paradigm. Learning and Individual Differences, 2025,118: 102602. https://doi.org/10.1016/j.lindif.2024.102602 doi: 10.1016/j.lindif.2024.102602
[4]	Bakker, A., Shvarts, A.Y., Abrahamson, D., Jankvist, U.T., van den Heuvel-Panhuizen, M. and Veldhuis, M., Generativity in design research: the case of developing a genre of action-based mathematics learning activities. Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education, 2023, 3096–3103.
[5]	Chen, J.A., J. Star, J.R., Dede, C. and Tutwiler, M.S., Technology-rich activities: One type does not motivate all. Contemporary Educational Psychology, 2018, 54: 153–170. https://doi.org/10.1016/j.cedpsych.2018.06.011 doi: 10.1016/j.cedpsych.2018.06.011
[6]	Foster, M.J., Shurtz, S. and Pepper, C., Evaluation of best practices in the design of online evidence-based practice instructional modules. J Med Libr Assoc, 2014,102(1): 31–40. https://doi.org/10.3163/1536-5050.102.1.007 doi: 10.3163/1536-5050.102.1.007
[7]	Linda, V., Xie, Y. and Han, M., Designing Visually Interactive Learning Modules to Promote Students' Critical Thinking in Mathematics. In 2018 IEEE Frontiers in Education Conference (FIE), 2018, 1–5. https://doi.org/10.1109/FIE.2018.8658568
[8]	Kemendikbudristek, 'Kurikulum Merdeka', ditpsd.kemdikbud.go.id. Accessed: Jun. 26, 2023. Available from: http://ditpsd.kemdikbud.go.id/hal/kurikulum-merdeka
[9]	Adnyani, L.P.W., Kurniawan, I. and Pinahayu, E.A.R., Development of creative-thinking instrument in mathematics problem solving based on logical mathematics intelligence. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 2018, 3(1): 1‒12. https://doi.org/10.23917/jramathedu.v3i1.5201 doi: 10.23917/jramathedu.v3i1.5201
[10]	Retnawati, H., Rafi, I., Mahmudi, A., Arliani, E., Zulnaidi, H., Abd Hamid, H.S., et al., A phenomenological study of challenges that prospective mathematics teachers face in developing mathematical problems that require higher-order thinking skills. EURASIA J Math Sci Tech Ed, 2023, 19(10): em2339. https://doi.org/10.29333/ejmste/13631 doi: 10.29333/ejmste/13631
[11]	Popham, M., Adams, S. and Hodge, J., Self-regulated strategy development to teach mathematics problem solving. Intervention in School and Clinic, 2020, 55(3): 154–161. https://doi.org/10.1177/1053451219842197 doi: 10.1177/1053451219842197
[12]	Newcombe, N.S., Seeing relationships: Using spatial thinking to teach science, mathematics, and social studies. American Educator, 2013, 37(1): 26.
[13]	Newcombe, N.S., Thinking spatially in the science classroom. Current Opinion in Behavioral Sciences, 2016, 10: 1–6. https://doi.org/10.1016/j.cobeha.2016.04.010 doi: 10.1016/j.cobeha.2016.04.010
[14]	Uttal, D.H., Meadow, N.G., Tipton, E., Hand, L.L., Alden, A.R., Warren, C., et al., The malleability of spatial skills: A meta-analysis of training studies. Psychological Bulletin, 2013,139(2): 352–402. https://doi.org/10.1037/a0028446 doi: 10.1037/a0028446
[15]	Wai, J. and Uttal, D.H., Why spatial reasoning matters for education policy. American Enterprise Institute, 2018.
[16]	Casey, B.M. and Fell, H., Spatial reasoning: A critical problem-solving tool in children's mathematics strategy tool-kit. Visualizing Mathematics: The Role of Spatial Reasoning in Mathematical Thought, 2018, 47–75. https://doi.org/10.1007/978-3-319-98767-5_3 doi: 10.1007/978-3-319-98767-5_3
[17]	Wei, W., Yuan, H., Chen, C. and Zhou, X., Cognitive correlates of performance in advanced mathematics. British Journal of Educational Psychology, 2012, 82(1): 157–181. https://doi.org/10.1111/j.2044-8279.2011.02049.x doi: 10.1111/j.2044-8279.2011.02049.x
[18]	Suggate, S. and Lenhard, W., Mental imagery skill predicts adults' reading performance. Learning and Instruction, 2022, 80: 101633. https://doi.org/10.1016/j.learninstruc.2022.101633 doi: 10.1016/j.learninstruc.2022.101633
[19]	Wang, S., Hu, B.Y. and Zhang, X., Kindergarteners' spatial skills and their reading and math achievement in second grade. Early Childhood Research Quarterly, 2021, 57: 156–166. https://doi.org/10.1016/j.ecresq.2021.06.002 doi: 10.1016/j.ecresq.2021.06.002
[20]	Gilligan, K.A., Flouri, E. and Farran, E.K., The contribution of spatial ability to mathematics achievement in middle childhood. Journal of Experimental Child Psychology, 2017,163: 107–125. https://doi.org/10.1016/j.jecp.2017.04.016 doi: 10.1016/j.jecp.2017.04.016
[21]	Patahuddin, S.M., Ramful, A., Lowrie, T. and Bholoa, A., Subtleties in spatial visualization maneuvers: Insights from numerical solutions. The Journal of Mathematical Behavior, 2022, 67: 100988. https://doi.org/10.1016/j.jmathb.2022.100988 doi: 10.1016/j.jmathb.2022.100988
[22]	Sorby, S., Veurink, N. and Streiner, S., Does spatial skills instruction improve STEM outcomes? The answer is "yes". Learning and Individual Differences, 2018, 67: 209–222. https://doi.org/10.1016/j.lindif.2018.09.001 doi: 10.1016/j.lindif.2018.09.001
[23]	Tam, Y.P. and Chan, W.W.L., The differential relations between sub-domains of spatial abilities and mathematical performance in children. Contemporary Educational Psychology, 2022, 71: 102101. https://doi.org/10.1016/j.cedpsych.2022.102101 doi: 10.1016/j.cedpsych.2022.102101
[24]	Gunderson, E.A. and Hildebrand, L., Relations among spatial skills, number line estimation, and exact and approximate calculation in young children. Journal of Experimental Child Psychology, 2021,212: 105251. https://doi.org/10.1016/j.jecp.2021.105251 doi: 10.1016/j.jecp.2021.105251
[25]	Kahl, T., Segerer, R., Grob, A. and Möhring, W., Bidirectional associations among executive functions, visual-spatial skills, and mathematical achievement in primary school students: Insights from a longitudinal study. Cognitive Development, 2022, 62: 101149. https://doi.org/10.1016/j.cogdev.2021.101149 doi: 10.1016/j.cogdev.2021.101149
[26]	Lowrie, T., Logan, T. and Hegarty, M., The influence of spatial visualization training on students' spatial reasoning and mathematics performance. Journal of Cognition and Development, 2019, 20(5): 729–751. https://doi.org/10.1080/15248372.2019.1653298 doi: 10.1080/15248372.2019.1653298
[27]	Putri, R.O.E., Spatial skill profile of mathematics pre-service teachers. J. Phys. Conf. Ser., 2018,947(1): 012065. https://doi.org/10.1088/1742-6596/947/1/012065 doi: 10.1088/1742-6596/947/1/012065
[28]	Putri, J.H., Syahputra, E. and Mulyono, M., Pengembangan media pembelajaran berbasis Macromedia Flash dengan menggunakan pembelajaran masalah untuk meningkatkan kemampuan spasial dan motivasi belajar siswa. PARADIKMA: JURNAL PENDIDIKAN MATEMATIKA, 2019, 12(2): 344918. https://doi.org/10.24114/paradikma.v12i3.22965 doi: 10.24114/paradikma.v12i3.22965
[29]	Battista, M.T., Frazee, L.M. and Winer, M.L., Analyzing the relation between spatial and geometric reasoning for elementary and middle school students. Visualizing Mathematics: The Role of Spatial Reasoning in Mathematical Thought, 2018,195–228. https://doi.org/10.1007/978-3-319-98767-5_10 doi: 10.1007/978-3-319-98767-5_10
[30]	Mix, K.S., Why are spatial skill and mathematics related?. Child Development Perspectives, 2019, 13(2): 121–126. https://doi.org/10.1111/cdep.12323 doi: 10.1111/cdep.12323
[31]	Mix, K.S. and Battista, M.T., Visualizing mathematics: The role of spatial reasoning in mathematical thought. Research in Mathematics Education, 2018. https://doi.org/10.1007/978-3-319-98767-5 doi: 10.1007/978-3-319-98767-5
[32]	Feriyanto, F. and Putri, R.O.E., Developing mathematics module based on literacy and Higher Order Thinking Skills (HOTS) questions to train critical thinking ability of high school students in Mojokerto. J. Phys. Conf. Ser., 2020, 1594(1): 012014. https://doi.org/10.1088/1742-6596/1594/1/012014 doi: 10.1088/1742-6596/1594/1/012014
[33]	Tari, F.A., Suwarma, I.R. and Hasanah, L., Development module of global warming issue to train Science, Technology, Engineering, and Mathematics (STEM) literacy. Journal of Innovative Science Education, 2023, 12(2): 141‒154. https://doi.org/10.15294/jise.v12i2.70525 doi: 10.15294/jise.v12i2.70525
[34]	Piaget, J. and Inhelder, B., The psychology of the child, Hachette UK, 2019.
[35]	Hjelte, A., Schindler, M. and Nilsson, P., Kinds of mathematical reasoning addressed in empirical research in mathematics education: A systematic review. Education Sciences, 2020, 10(10): 289. https://doi.org/10.3390/educsci10100289 doi: 10.3390/educsci10100289
[36]	Clements, D.H. and Sarama, J., Learning and teaching early math: The learning trajectories approach, Routledge, 2020. https://doi.org/10.4324/9781003083528
[37]	Newcombe, N.S., Picture this: Increasing math and science learning by improving spatial thinking. American Educator, 2010, 34(2): 29.
[38]	Gilligan-Lee, K.A., Hawes, Z.C.K. and Mix, K.S., Spatial thinking as the missing piece in mathematics curricula. npj Sci. Learn., 2022, 7(1): 10. https://doi.org/10.1038/s41539-022-00128-9 doi: 10.1038/s41539-022-00128-9
[39]	Newcombe, N.S., Uttal, D.H. and Sauter, M., Spatial development. In The Oxford handbook of developmental psychology (Vol 1): Body and mind, in Oxford library of psychology, New York, NY, US: Oxford University Press, 2013,564–590. https://doi.org/10.1093/oxfordhb/9780199958450.013.0020
[40]	Mulligan, J., Woolcott, G., Mitchelmore, M. and Davis, B., Connecting mathematics learning through spatial reasoning. Math Ed Res J, 2018, 30(1): 77–87. https://doi.org/10.1007/s13394-017-0210-x doi: 10.1007/s13394-017-0210-x
[41]	Schoenfeld, A., Reflections on problem solving theory and practice. The Mathematics Enthusiast, 2013, 10(1): 9–34. https://doi.org/10.54870/1551-3440.1258 doi: 10.54870/1551-3440.1258
[42]	Cheng, Y.L. and Mix, K.S., Spatial Training Improves Children's Mathematics Ability. Journal of Cognition and Development, 2014, 15(1): 2–11. https://doi.org/10.1080/15248372.2012.725186 doi: 10.1080/15248372.2012.725186
[43]	Cohen, L., Manion, L. and Morrison, K., Research methods in education, 8th edn, London: Routledge, 2017. https://doi.org/10.4324/9781315456539
[44]	Ramful, A., Lowrie, T. and Logan, T., Measurement of spatial ability: Construction and validation of the spatial reasoning instrument for middle school students. Journal of Psychoeducational Assessment, 2017, 35(7): 709–727. https://doi.org/10.1177/0734282916659207 doi: 10.1177/0734282916659207
[45]	OECD, PISA 2018 results (Volume I): What students know and can do. in PISA. OECD, 2019. https://doi.org/10.1787/5f07c754-en
[46]	OECD, PISA 2022 assessment and analytical framework. Paris: Organisation for Economic Co-operation and Development, 2023. Accessed: Jan. 18, 2024. Available from: https://www.oecd-ilibrary.org/fr/education/pisa-2022-assessment-and-analytical-framework_dfe0bf9c-en
[47]	Aiken, L.R., Relationships between the item difficulty and discrimination indexes. Educational and Psychological Measurement, 1979, 39(4): 821–824. https://doi.org/10.1177/001316447903900415 doi: 10.1177/001316447903900415
[48]	Hastuti, T.A., Sari, I.P.T.P. and Andrianto, S.D., Analysis of the Aiken index to know the content validity of the lesson plan evaluation instrument on physical fitness materials viewed from learning strategies. 6th Yogyakarta International Seminar on Health, Physical Education and Sport Science (YISHPESS 2023), 2023,276–282. Atlantis Press. https://doi.org/10.2991/978-94-6463-356-6_31
[49]	Mallery Paul, D.G., IBM SPSS statistics 26 step by step: A simple guide and reference, 16th edn. New York: Routledge, 2019. https://doi.org/10.4324/9780429056765
[50]	Francis, K., Rothschuh, S., Poscente, D. and Davis, B., Malleability of spatial reasoning with short-term and long-term robotics interventions. Tech Know Learn, 2022, 27(3): 927–956. https://doi.org/10.1007/s10758-021-09520-7 doi: 10.1007/s10758-021-09520-7
[51]	Yuanita, P., Zulnaidi, H. and Zakaria, E., The effectiveness of Realistic Mathematics Education approach: The role of mathematical representation as mediator between mathematical belief and problem solving. PLOS ONE, 2018, 13(9): e0204847. https://doi.org/10.1371/journal.pone.0204847 doi: 10.1371/journal.pone.0204847
[52]	Chua, Y.P., Kaedah dan statistik penyelidikan: Asas statistik penyelidikan : buku 2. McGraw-Hill, 2006.
[53]	Leech, N.L., Barrett, K.C. and Morgan, G.A., IBM SPSS for intermediate statistics: Use and interpretation, fourth edition. Routledge, 2012.
[54]	Hidayah, N., Komikesari, H., Pratiwi, W.O., Asiah, N., Asyhari, A. and Yusandika, A.D., 'STEM-based science E-module: Is it sufficient to improve students' creative thinking skills?. AIP Conference Proceedings, 2023, 2595(1): 040016. https://doi.org/10.1063/5.0124234 doi: 10.1063/5.0124234
[55]	Kuit, V.K. and Osman, K., CHEMBOND3D e-module effectiveness in enhancing students' knowledge of chemical bonding concept and visual-spatial skills. EUR J SCI MATH ED, 2021, 9(4): 252–264. https://doi.org/10.30935/scimath/11263 doi: 10.30935/scimath/11263
[56]	Moradi, M., Liu, L., Luchies, C., Patterson, M.M. and Darban, B., Enhancing teaching-learning effectiveness by creating online interactive instructional modules for fundamental concepts of physics and mathematics. Education Sciences, 2018, 8(3): 109. https://doi.org/10.3390/educsci8030109 doi: 10.3390/educsci8030109
[57]	Eroğlu, D., A virtual manipulative to support rural students in developing spatial skills in online distance education: Isometric drawing tool. Necmettin Erbakan Üniversitesi Ereğli Eğitim Fakültesi Dergisi, 2023,153‒190.
[58]	Sugiarni, R., Alghifari, E. and Ifanda, A.R., Meningkatkan kemampuan spasial matematis siswa dengan model pembelajaran problem based learning berbantuan Geogebra. Kalamatika: Jurnal Pendidikan Matematika, 2018, 3(1): 93‒102. https://doi.org/10.22236/KALAMATIKA.vol3no1.2018pp93-102 doi: 10.22236/KALAMATIKA.vol3no1.2018pp93-102
[59]	Tamam, B. and D. Dasari, D., The use of Geogebra software in teaching mathematics. J. Phys. Conf. Ser., 2021, 1882(1): 012042. https://doi.org/10.1088/1742-6596/1882/1/012042 doi: 10.1088/1742-6596/1882/1/012042
[60]	Winarti, D.W., Patahuddin, S.M. and Lowrie, T., Unleashing the potential: spatializing middle school mathematics for enhanced learning. Educ Stud Math, 2024,117(3): 419–439. https://doi.org/10.1007/s10649-024-10343-3 doi: 10.1007/s10649-024-10343-3
[61]	Lawson, M.J. and Chinnappan, M., Knowledge connectedness in Geometry problem solving. Journal for research in mathematics education, 2000, 31(1): 26‒43. https://doi.org/10.2307/749818 doi: 10.2307/749818
[62]	Hwang, W.Y., Purba, S.W.D., Liu, Y., Zhang, Y.Y. and Chen, N.S., An investigation of the effects of measuring authentic contexts on geometry learning achievement. IEEE Transactions on Learning Technologies, 2019, 12(3): 291–302. https://doi.org/10.1109/TLT.2018.2853750 doi: 10.1109/TLT.2018.2853750
[63]	Hawes, Z., Moss, J., Caswell, B., Naqvi, S. and MacKinnon, S., Enhancing children's spatial and numerical skills through a dynamic spatial approach to early Geometry instruction: Effects of a 32-week intervention. Cognition and Instruction, 2017, 35(3): 236–264. https://doi.org/10.1080/07370008.2017.1323902 doi: 10.1080/07370008.2017.1323902
[64]	Clements, D.H., Sarama, J., Swaminathan, S., Weber, D. and Trawick-Smith, J., Teaching and learning Geometry: early foundations. Quadrante, 2018, 27(2): 7–31. https://doi.org/10.48489/quadrante.22970 doi: 10.48489/quadrante.22970

Author's biography Rizky Oktaviana Eko Putri is a doctoral student in the Department of Mathematics and Science Education at the Faculty of Education, Universiti Malaya. Her research interests include mathematics education, educational technologies, spatial reasoning, and cognitive skills; Assoc. Prof. Dr. Hutkemri Zulnaidi is an Associate Professor in the Department of Mathematics and Science Education at the Faculty of Education, Universiti Malaya. His specialties include mathematics education, educational technology, problem solving, assessment and measurement, statistics, and quantitative research methods. He is currently involved in several research projects related to Industrial Revolution 4.0, lifelong learning, teaching innovation, learning support, burnout, soft skills, and teaching practices. He also actively participates in research workshops on statistical data analysis (using SPSS, AMOS, and SmartPLS) and research methodology; Dr. Suzieleez Syrene Abdul Rahim is a senior lecturer in the Department of Mathematics and Science Education at the Faculty of Education, Universiti Malaya. Her specialties include mathematics education, teaching and learning, assessment, pedagogy, teachers' beliefs, qualitative research, and teacher development

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