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Abstract
Spatial reasoning is essential for success in mathematics and STEM fields, yet it is often overlooked in primary school curricula. This study investigates the levels and progression of spatial reasoning abilities among primary school students in Indonesia, focusing on mental rotation, spatial orientation, and spatial visualization. A cross-sectional study involving 135 students from Year 2, Year 4, and Year 6 used an adapted Spatial Reasoning Instrument. Results showed below-average spatial reasoning abilities overall, with notable improvement with age: Year 2 students averaged a Spatial Reasoning Test Score (SRTS) of 1.66, Year 4 students 2.02, and Year 6 students 2.68. Challenges were identified in tasks requiring multi-step spatial reasoning, spatial language comprehension, and 2D-3D transformations, particularly among younger students. These findings highlight the need for curriculum enhancements and targeted interventions to develop spatial reasoning skills from an early age, improving academic performance in STEM subjects.
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Copyright (c) 2024 uswatun hasanah, Susilahudin Putrawangsa, Edi Purwanta, Farida Agus Setiawati, Yoppy Wahyu Purnomo
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References
- Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52(3), 215-241. https://doi.org/10.1023/A:1024312321077.
- Bakker, A., & Hoffmann, M. H. G. (2005). Diagrammatic Reasoning as the Basis for Developing Concepts: A Semiotic Analysis of Students' Learning about Statistical Distribution. Educational Studies in Mathematics, 60(3), 333-358. https://doi.org/10.1007/s10649-005-5536-8.
- Boonen, A. J. H., van Wesel, F., Jolles, J., & van der Schoot, M. (2014). The role of visual representation type, spatial ability, and reading comprehension in word problem solving: An item-level analysis in elementary school children. International Journal of Educational Research, 68, 15—26. https://doi.org/10.1016/j.ijer.2014.08.001
- Bower, C. A., Foster, L., Zimmermann, L., Verdine, B. N., Marzouk, M., Islam, S., Golinkoff, R. M., & Hirsh-Pasek, K. (2020). Three-year-olds’ spatial language comprehension and links with mathematics and spatial performance. Developmental Psychology, 56, 1894-1905. https://doi.org/10.1037/dev0001098
- Bruce, C., Sinclair, N., Moss, J., Hawes, Z., & Caswell, B. (2015). Spatializing the curriculum. In B. Davis & T. S. R. S. Group (Eds.), Spatial reasoning in the early years: Principles, assertion, and speculation. Routledge, Taylor & Francis Group. https://doi.org/10.4324/9781315762371
- Creswell, J. W., & Creswell, J. D. (2023). Research design: Qualitative, quantitative, and mixed methods approaches (6th ed.). Sage Publications.
- Davis, B., Drefs, M., & Francis, K. (2015a). A history and analysis of current curriculum. In Spatial reasoning in the early years: Principles, assertions, and speculations (pp. 47-62). Routledge. https://doi.org/10.4324/9781315762371
- Davis, B., Okamoto, Y., & Whiteley, W. (2015b). Spatializing school mathematics. In B. Davis & T. S. R. S. Group (Eds.), Spatial Reasoning in the early years: Principles, assertions, and speculations. Routledge. https://doi.org/10.4324/9781315762371
- Davis, B., & Spatial Reasoning Study Group, T. (2015c). Spatial reasoning in the early years. Routledge. https://doi.org/10.4324/9781315762371
- Francis, K., & Whiteley, W. (2015). Interactions between three dimensions and two dimensions. In Spatial Reasoning in the Early Years (pp. 121-136). Routledge. https://doi.org/10.4324/9781315762371
- Fujita, T., Kondo, Y., Kumakura, H., Kunimune, S., & Jones, K. (2020). Spatial reasoning skills about 2D representations of 3D geometrical shapes in grades 4 to 9. Mathematics Education Research Journal, 32(2), 235-255. https://doi.org/10.1007/s13394-020-00335-w
- Giacomone, B., Godino, J. D., Blanco, T. F., & Wilhelmi, M. R. (2022). Onto-semiotic Analysis of Diagrammatic Reasoning. International Journal of Science and Mathematics Education. https://doi.org/10.1007/s10763-022-10316-z
- Gilligan-Lee, K. A., Hodgkiss, A., Thomas, M. S. C., Patel, P. K., & Farran, E. K. (2021). Aged-based differences in spatial language skills from 6 to 10 years: Relations with spatial and mathematics skills. Learning and Instruction, 73, 101417. https://doi.org/https://doi.org/10.1016/j.learninstruc.2020.101417
- Hawes, Z. C. K., Gilligan-Lee, K. A., & Mix, K. S. (2022). Effects of spatial training on mathematics performance: A meta-analysis. Developmental Psychology, 58, 112—137. https://doi.org/10.1037/dev0001281
- Hegarty, M., Crookes, R. D., Dara-Abrams, D., & Shipley, T. F. (2010). Do All Science Disciplines Rely on Spatial Abilities? Preliminary Evidence from Self-report Questionnaires. Spatial Cognition VII, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14749-4_10
- Hegarty, M., & Kozhevnikov, M. (1999). Types of visual–spatial representations and mathematical problem solving. Journal of educational psychology, 91(4), 684–689. https://doi.org/10.1037/0022-0663.91.4.684
- Hodgkiss, A., Gilligan-Lee, K. A., Thomas, M. S. C., Tolmie, A. K., & Farran, E. K. (2021). The developmental trajectories of spatial skills in middle childhood. Br J Dev Psychol, 39(4), 566-583. https://doi.org/10.1111/bjdp.12380
- Ishikawa, T., & Kastens, K. A. (2005). Why Some Students Have Trouble with Maps and Other Spatial Representations. Journal of Geoscience Education, 53(2), 184-197. https://doi.org/10.5408/1089-9995-53.2.184
- Jirout, J. J., & Newcombe, N. S. (2015). Building Blocks for Developing Spatial Skills: Evidence From a Large, Representative U.S. Sample. Psychological Science, 26(3), 302-310. https://doi.org/10.1177/0956797614563338
- Lowrie, T. (2001). The influence of visual representations on mathematical problem solving and numeracy performance The 24th Annual MERGA Conference, Sydney. https://catalogue.nla.gov.au/catalog/5683988
- Lowrie, T. (2002). The Influence of Visual and Spatial Reasoning in Interpreting Simulated 3D Worlds. International Journal of Computers for Mathematical Learning, 7(3), 301-318. https://doi.org/10.1023/A:1022116221735
- Lowrie, T., Harris, D., Logan, T., & Hegarty, M. (2021). The impact of a spatial intervention program on students’ spatial reasoning and mathematics performance. The Journal of Experimental Education, 89(2), 259—277. https://doi.org/10.1080/00220973.2019.1684869
- Lowrie, T., & Logan, T. (2018a). The interaction between spatial reasoning constructs and mathematics understandings in elementary classrooms. In K. S. Mix & M. T. Battista (Eds.), Visualizing mathematics: The role of spatial reasoning in mathematical thought (pp. 253—276). Springer. https://doi.org/10.1007/978-3-319-98767-5_12
- Lowrie, T., & Logan, T. (2018b). Part I Commentary 3: Proposing a Pedagogical Framework for the Teaching and Learning of Spatial Skills: A Commentary on Three Chapters. In Visualizing Mathematics (pp. 171-182). Springer. https://doi.org/10.1007/978-3-319-98767-5_8
- Lowrie, T., Logan, T., & Hegarty, M. (2019). The influence of spatial visualization training on students’ spatial reasoning and mathematics performance. Journal of Cognition and Development, 20(5), 729—751. https://doi.org/10.1080/15248372.2019.1653298
- Lowrie, T., Logan, T., & Ramful, A. (2017). Visuospatial training improves elementary students' mathematics performance. British Journal of Educational Psychology, 87(2), 170—186. https://doi.org/10.1111/bjep.12142
- Newcombe, N. S. (2010). Picture this: Increasing math and science learning by improving spatial thinking. American educator, 34(2), 29.
- Okamoto, Y., Kotsopoulos, D., McGarvey, L., & Hallowell, D. (2015). The development of spatial reasoning in young children. In Spatial reasoning in the early years (pp. 15-28). Routledge. https://doi.org/10.4324/9781315762371
- Putrawangsa, S., Febrian, F., & Hasanah, U. (2021). Developing students’ understanding of percentage: The role of spatial representation. Mathematics Teaching Research Journal, 13(4—26). https://commons.hostos.cuny.edu/mtrj/archives/volume-13-n-4/
- Putrawangsa, S., & Hasanah, U. (2022). The potential of spatial reasoning in mediating mathematical understanding: The case of number line AIP Conference Proceedings, https://doi.org/10.1063/5.0099540
- Putrawangsa, S., & Patahuddin, S. (2022). Embodied task to promote spatial seasoning and early understanding of multiplication The 44th Annual Conference of the Mathematics Education Research Group of Australasia, Launceston. https://merga.net.au/Public/Publications/Annual_Conference_Proceedings/2022-Conference-Proceedings-.aspx
- 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), 709-727. https://psycnet.apa.org/doi/10.1177/0734282916659207
- Rivera, F. D. (2011). Toward a visually oriented school mathematics curriculum: Research, theory, practice, and issues. Springer. https://doi.org/10.1007/978-94-007-0014-7
- Schifter, D., Monk, S., Russel, S. J., & Bastable, V. (2008). Early algebra: What does understanding of laws of arithmetic mean in the elementary grades? . In J. J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp. 211—234). Routledge. https://doi.org/10.4324/9781315097435
- Stieff, M., & Uttal, D. (2015). How Much Can Spatial Training Improve STEM Achievement? Educational Psychology Review, 27(4), 607-615. https://doi.org/10.1007/s10648-015-9304-8
- Tessler, S., Iwasaki, Y., & Law, K. H. (1996). REDRAW — a diagrammatic reasoning system for qualitative structural analysis. Advances in Engineering Software, 25(2), 149-159. https://doi.org/https://doi.org/10.1016/0965-9978(95)00098-4
- Uttal, D. H., Meadow, N. G., Tipton, E., Hand, L. L., Alden, A. R., Warren, C., & Newcombe, N. S. (2013a). The Malleability of Spatial Skills: A Meta-Analysis of Training Studies. Psychological bulletin, 139(2), 352-402. https://doi.org/10.1037/a0028446
- Uttal, D. H., Miller, D. I., & Newcombe, N. S. (2013b). Exploring and Enhancing Spatial Thinking:Links to Achievement in Science, Technology, Engineering, and Mathematics? Current Directions in Psychological Science, 22(5), 367-373. http://dx.doi.org/10.1177/0963721413484756
- Woolcott, G., Le Tran, T., Mulligan, J., Davis, B., & Mitchelmore, M. (2022). Towards a framework for spatial reasoning and primary mathematics learning: an analytical synthesis of intervention studies. Mathematics Education Research Journal, 34(1), 37-67. https://doi.org/10.1007/s13394-020-00318-x
References
Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52(3), 215-241. https://doi.org/10.1023/A:1024312321077.
Bakker, A., & Hoffmann, M. H. G. (2005). Diagrammatic Reasoning as the Basis for Developing Concepts: A Semiotic Analysis of Students' Learning about Statistical Distribution. Educational Studies in Mathematics, 60(3), 333-358. https://doi.org/10.1007/s10649-005-5536-8.
Boonen, A. J. H., van Wesel, F., Jolles, J., & van der Schoot, M. (2014). The role of visual representation type, spatial ability, and reading comprehension in word problem solving: An item-level analysis in elementary school children. International Journal of Educational Research, 68, 15—26. https://doi.org/10.1016/j.ijer.2014.08.001
Bower, C. A., Foster, L., Zimmermann, L., Verdine, B. N., Marzouk, M., Islam, S., Golinkoff, R. M., & Hirsh-Pasek, K. (2020). Three-year-olds’ spatial language comprehension and links with mathematics and spatial performance. Developmental Psychology, 56, 1894-1905. https://doi.org/10.1037/dev0001098
Bruce, C., Sinclair, N., Moss, J., Hawes, Z., & Caswell, B. (2015). Spatializing the curriculum. In B. Davis & T. S. R. S. Group (Eds.), Spatial reasoning in the early years: Principles, assertion, and speculation. Routledge, Taylor & Francis Group. https://doi.org/10.4324/9781315762371
Creswell, J. W., & Creswell, J. D. (2023). Research design: Qualitative, quantitative, and mixed methods approaches (6th ed.). Sage Publications.
Davis, B., Drefs, M., & Francis, K. (2015a). A history and analysis of current curriculum. In Spatial reasoning in the early years: Principles, assertions, and speculations (pp. 47-62). Routledge. https://doi.org/10.4324/9781315762371
Davis, B., Okamoto, Y., & Whiteley, W. (2015b). Spatializing school mathematics. In B. Davis & T. S. R. S. Group (Eds.), Spatial Reasoning in the early years: Principles, assertions, and speculations. Routledge. https://doi.org/10.4324/9781315762371
Davis, B., & Spatial Reasoning Study Group, T. (2015c). Spatial reasoning in the early years. Routledge. https://doi.org/10.4324/9781315762371
Francis, K., & Whiteley, W. (2015). Interactions between three dimensions and two dimensions. In Spatial Reasoning in the Early Years (pp. 121-136). Routledge. https://doi.org/10.4324/9781315762371
Fujita, T., Kondo, Y., Kumakura, H., Kunimune, S., & Jones, K. (2020). Spatial reasoning skills about 2D representations of 3D geometrical shapes in grades 4 to 9. Mathematics Education Research Journal, 32(2), 235-255. https://doi.org/10.1007/s13394-020-00335-w
Giacomone, B., Godino, J. D., Blanco, T. F., & Wilhelmi, M. R. (2022). Onto-semiotic Analysis of Diagrammatic Reasoning. International Journal of Science and Mathematics Education. https://doi.org/10.1007/s10763-022-10316-z
Gilligan-Lee, K. A., Hodgkiss, A., Thomas, M. S. C., Patel, P. K., & Farran, E. K. (2021). Aged-based differences in spatial language skills from 6 to 10 years: Relations with spatial and mathematics skills. Learning and Instruction, 73, 101417. https://doi.org/https://doi.org/10.1016/j.learninstruc.2020.101417
Hawes, Z. C. K., Gilligan-Lee, K. A., & Mix, K. S. (2022). Effects of spatial training on mathematics performance: A meta-analysis. Developmental Psychology, 58, 112—137. https://doi.org/10.1037/dev0001281
Hegarty, M., Crookes, R. D., Dara-Abrams, D., & Shipley, T. F. (2010). Do All Science Disciplines Rely on Spatial Abilities? Preliminary Evidence from Self-report Questionnaires. Spatial Cognition VII, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14749-4_10
Hegarty, M., & Kozhevnikov, M. (1999). Types of visual–spatial representations and mathematical problem solving. Journal of educational psychology, 91(4), 684–689. https://doi.org/10.1037/0022-0663.91.4.684
Hodgkiss, A., Gilligan-Lee, K. A., Thomas, M. S. C., Tolmie, A. K., & Farran, E. K. (2021). The developmental trajectories of spatial skills in middle childhood. Br J Dev Psychol, 39(4), 566-583. https://doi.org/10.1111/bjdp.12380
Ishikawa, T., & Kastens, K. A. (2005). Why Some Students Have Trouble with Maps and Other Spatial Representations. Journal of Geoscience Education, 53(2), 184-197. https://doi.org/10.5408/1089-9995-53.2.184
Jirout, J. J., & Newcombe, N. S. (2015). Building Blocks for Developing Spatial Skills: Evidence From a Large, Representative U.S. Sample. Psychological Science, 26(3), 302-310. https://doi.org/10.1177/0956797614563338
Lowrie, T. (2001). The influence of visual representations on mathematical problem solving and numeracy performance The 24th Annual MERGA Conference, Sydney. https://catalogue.nla.gov.au/catalog/5683988
Lowrie, T. (2002). The Influence of Visual and Spatial Reasoning in Interpreting Simulated 3D Worlds. International Journal of Computers for Mathematical Learning, 7(3), 301-318. https://doi.org/10.1023/A:1022116221735
Lowrie, T., Harris, D., Logan, T., & Hegarty, M. (2021). The impact of a spatial intervention program on students’ spatial reasoning and mathematics performance. The Journal of Experimental Education, 89(2), 259—277. https://doi.org/10.1080/00220973.2019.1684869
Lowrie, T., & Logan, T. (2018a). The interaction between spatial reasoning constructs and mathematics understandings in elementary classrooms. In K. S. Mix & M. T. Battista (Eds.), Visualizing mathematics: The role of spatial reasoning in mathematical thought (pp. 253—276). Springer. https://doi.org/10.1007/978-3-319-98767-5_12
Lowrie, T., & Logan, T. (2018b). Part I Commentary 3: Proposing a Pedagogical Framework for the Teaching and Learning of Spatial Skills: A Commentary on Three Chapters. In Visualizing Mathematics (pp. 171-182). Springer. https://doi.org/10.1007/978-3-319-98767-5_8
Lowrie, T., Logan, T., & Hegarty, M. (2019). The influence of spatial visualization training on students’ spatial reasoning and mathematics performance. Journal of Cognition and Development, 20(5), 729—751. https://doi.org/10.1080/15248372.2019.1653298
Lowrie, T., Logan, T., & Ramful, A. (2017). Visuospatial training improves elementary students' mathematics performance. British Journal of Educational Psychology, 87(2), 170—186. https://doi.org/10.1111/bjep.12142
Newcombe, N. S. (2010). Picture this: Increasing math and science learning by improving spatial thinking. American educator, 34(2), 29.
Okamoto, Y., Kotsopoulos, D., McGarvey, L., & Hallowell, D. (2015). The development of spatial reasoning in young children. In Spatial reasoning in the early years (pp. 15-28). Routledge. https://doi.org/10.4324/9781315762371
Putrawangsa, S., Febrian, F., & Hasanah, U. (2021). Developing students’ understanding of percentage: The role of spatial representation. Mathematics Teaching Research Journal, 13(4—26). https://commons.hostos.cuny.edu/mtrj/archives/volume-13-n-4/
Putrawangsa, S., & Hasanah, U. (2022). The potential of spatial reasoning in mediating mathematical understanding: The case of number line AIP Conference Proceedings, https://doi.org/10.1063/5.0099540
Putrawangsa, S., & Patahuddin, S. (2022). Embodied task to promote spatial seasoning and early understanding of multiplication The 44th Annual Conference of the Mathematics Education Research Group of Australasia, Launceston. https://merga.net.au/Public/Publications/Annual_Conference_Proceedings/2022-Conference-Proceedings-.aspx
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), 709-727. https://psycnet.apa.org/doi/10.1177/0734282916659207
Rivera, F. D. (2011). Toward a visually oriented school mathematics curriculum: Research, theory, practice, and issues. Springer. https://doi.org/10.1007/978-94-007-0014-7
Schifter, D., Monk, S., Russel, S. J., & Bastable, V. (2008). Early algebra: What does understanding of laws of arithmetic mean in the elementary grades? . In J. J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp. 211—234). Routledge. https://doi.org/10.4324/9781315097435
Stieff, M., & Uttal, D. (2015). How Much Can Spatial Training Improve STEM Achievement? Educational Psychology Review, 27(4), 607-615. https://doi.org/10.1007/s10648-015-9304-8
Tessler, S., Iwasaki, Y., & Law, K. H. (1996). REDRAW — a diagrammatic reasoning system for qualitative structural analysis. Advances in Engineering Software, 25(2), 149-159. https://doi.org/https://doi.org/10.1016/0965-9978(95)00098-4
Uttal, D. H., Meadow, N. G., Tipton, E., Hand, L. L., Alden, A. R., Warren, C., & Newcombe, N. S. (2013a). The Malleability of Spatial Skills: A Meta-Analysis of Training Studies. Psychological bulletin, 139(2), 352-402. https://doi.org/10.1037/a0028446
Uttal, D. H., Miller, D. I., & Newcombe, N. S. (2013b). Exploring and Enhancing Spatial Thinking:Links to Achievement in Science, Technology, Engineering, and Mathematics? Current Directions in Psychological Science, 22(5), 367-373. http://dx.doi.org/10.1177/0963721413484756
Woolcott, G., Le Tran, T., Mulligan, J., Davis, B., & Mitchelmore, M. (2022). Towards a framework for spatial reasoning and primary mathematics learning: an analytical synthesis of intervention studies. Mathematics Education Research Journal, 34(1), 37-67. https://doi.org/10.1007/s13394-020-00318-x