Spatial Reasoning of Students With Mathematical Learning Difficulties
Abstract
Spatial reasoning is essential for solving two or three-dimensional oriented problems. Meanwhile, primary school students often experience mathematical learning difficulties (MLD) using spatial reasoning. The research analyzes the spatial reasoning of primary school students who experience MLD. The research method is qualitative, with the research subject being fifth-grade students at one of the primary schools in Sidoarjo. The research instruments used spatial reasoning tests and interview guidelines. The results stated differences in spatial reasoning in students' MLD types. Students who experience visual spatial type MLD have lower spatial reasoning skills because they cannot solve spatial orientation, mental rotation, and spatial visualization problems. Meanwhile, students who experience memory-type MLD have moderate spatial reasoning because they can solve spatial orientation and spatial visualization problems but cannot solve mental rotation problems. The researcher suggested that the subsequent research should intervene in the spatial reasoning of students who experience MLD.
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References
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Beswick, K. (2008). Influencing teachers’ beliefs about teaching mathematics for numeracy to students with mathematics learning difficulties. Mathematics Teacher Education and Development, 9(2000), 3–20. http://ecite.utas.edu.au/55228/1/MTED_9_Beswick.pdf
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
Chinn, S. (2014). The routledge international handbook of dyscalculia and mathematical learning difficulties. In The Routledge International Handbook of Dyscalculia and Mathematical Learning Difficulties. https://doi.org/10.4324/9781315740713
Clements, D. H., Germeroth, C., & Sovran, B. (2015). The Building Blocks of Mathematics for Infants and Toddlers: An Annotated Bibliography for Course Developers 2015.
Creswell, J. W. (2014). Research design: Qualitative, quantitative, and mixed methods approaches. SAGE Publications. https://books.google.co.id/books?id=4uB76IC_pOQC
De Smedt, B., Taylor, J., Archibald, L., & Ansari, D. (2010). How is phonological processing related to individual differences in children’s arithmetic skills? Developmental Science, 13(3), 508–520. https://doi.org/10.1111/j.1467-7687.2009.00897.x
Dimitriu, D. G., & Dimitriu, D. C. (2020). A simple method to help students improve 3-D visualization skills. ASEE Annual Conference and Exposition, Conference Proceedings, 2020-June.
Dintarini, M., Jamil, A. F., & Ismail, A. D. (2022). Secondary students’ spatial thinking in solving the minimum competency assessment (MCA) on geometry. Jurnal Elemen, 8(2), 544–555. https://doi.org/10.29408/jel.v8i2.5670
Donnelly, E. L. H. (2021). Exploring the spatial-math link: The impact of tailored visual memory interventions for children with MLD. https://prism.ucalgary.ca/handle/1880/112974%0Ahttps://prism.ucalgary.ca/bitstream/handle/1880/112974/ucalgary_2021_donnelly_emma.pdf?sequence=2&isAllowed=y
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
Gunderson, E. A., Ramirez, G., Beilock, S. L., & Levine, S. C. (2012). The relation between spatial skill and early number knowledge: The role of the linear number line. Developmental Psychology, 48(5), 1229–1241. https://doi.org/10.1037/a0027433
Hamukwaya, S. T., & Haser, Ç. (2021). “It does not mean that they cannot do mathematics”: Beliefs about Mathematics Learning Difficulties. International Electronic Journal of Mathematics Education, 16(1), em0622. https://doi.org/10.29333/iejme/9569
Hasanah, U., & Kumoro, D. T. (2021). Kemampuan spasial: Kajian pada siswa usia sekolah dasar. Jurnal Pacu Pendidikan Dasar, 1(1), 27–34. https://unu-ntb.e-journal.id/pacu/article/view/68/19
Hawes, Z., Moss, J., Caswell, B., Naqvi, S., & MacKinnon, S. (2017). 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, 35(3), 236–264. https://doi.org/10.1080/07370008.2017.1323902
Karagiannakis, G., Baccaglini-frank, A., & Papadatos, Y. (2014). Mathematical learning difficulties subtypes classification. Frontiers in Human Neuroscience, 8(February), 1–5. https://doi.org/10.3389/fnhum.2014.00057
Khine, M. S. (2017). Visual-spatial ability in STEM education. In Visual-spatial Ability in STEM Education. https://doi.org/10.1007/978-3-319-44385-0
Kusuma, A. P., Rochmad, & Isnarto. (2021). Penerapan model accelerated learning cycle terhadap penalaran matematis ditinjau dari kemampuan spasial. PRISMA, Prosiding Seminar Nasional Matematika, 4(1), 75–79. https://journal.unnes.ac.id/sju/index.php/prisma/article/view/44952
Lestari, D. D. P., Budiarto, M. T., & Lukito, A. (2021). Analisis kemampuan spatial visualization siswa sekolah dasar dalam pemecahan masalah geometri: Ditinjau dari kemampuan matematika tingkat tinggi. ELSE (Elementary School Education Journal)?: Jurnal Pendidikan Dan Pembelajaran Sekolah Dasar, 5(1), 55. https://doi.org/10.30651/else.v5i1.7371
Levy, S., Turk-Browne, N. B., & Goldfarb, L. (2023). Impaired visuo-spatial statistical learning with mathematical learning difficulties. Visual Cognition, May. https://doi.org/10.1080/13506285.2023.2208887
Lowrie, T., Logan, T., Harris, D., & Hegarty, M. (2018). The impact of an intervention program on students’ spatial reasoning: student engagement through mathematics-enhanced learning activities. Cognitive Research: Principles and Implications, 3(1), 1–10. https://doi.org/10.1186/s41235-018-0147-y
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
Ma’rifatin, S., Amin, S. M., & Siswono, T. Y. E. (2019). Students’ mathematical ability and spatial reasoning in solving geometric problem. Journal of Physics: Conference Series, 1157(4). https://doi.org/10.1088/1742-6596/1157/4/042062
Mazzocco, M. M. M. (2009). An introduction to the special issue: Pathways to mathematical learning difficulties and disabilities. Developmental Disabilities Research Reviews, 15(1), 1–3. https://doi.org/10.1002/ddrr.52
Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative data analysis. SAGE Publications. https://books.google.co.id/books?id=3CNrUbTu6CsC
Murphy, M. M., Mazzocco, M. M. M., Hanich, L. B., & Early, M. C. (2007). Cognitive characteristics of children with mathematics learning disability (MLD) vary as a function of the cutoff criterion used to define MLD. Journal of Learning Disabilities, 40(5), 458–478.
Musriroh, R. Z., Hidayanto, E., & Rahardi, R. (2021). Penalaran spasial matematis dimensi persepsi dan visualisasi kelas VIII dalam pemecahan masalah geometri. Jurnal Pendidikan: Teori, Penelitian, Dan Pengembangan, 6(11), 1774. https://doi.org/10.17977/jptpp.v6i11.15144
Pavlovicova, G., & SvecovA, V. (2015). The development of spatial skills through discovering in the geometrical education at primary school. Procedia - Social and Behavioral Sciences, 186, 990–997. https://doi.org/10.1016/j.sbspro.2015.04.189
Pittalis, M., & Christou, C. (2010). Types of reasoning in 3D geometry thinking and their relation with spatial ability. Educational Studies in Mathematics, 75(2), 191–212. https://doi.org/10.1007/s10649-010-9251-8
Plerou, A., & Vlamos, P. (2016). Algorithmic thinking and mathematical learning difficulties classification. American Journal of Applied Psychology, 5(5), 22. https://doi.org/10.11648/j.ajap.20160505.11
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://doi.org/10.1177/0734282916659207
Skagerlund, K., & Träff, U. (2014). Development of magnitude processing in children with developmental dyscalculia: Space, time, and number. Frontiers in Psychology, 5(JUN), 1–16. https://doi.org/10.3389/fpsyg.2014.00675
Szucs, D., Devine, A., Soltesz, F., Nobes, A., & Gabriel, F. (2013). Developmental dyscalculia is related to visuo-spatial memory and inhibition impairment. Cortex, 49(10), 2674–2688. https://doi.org/10.1016/j.cortex.2013.06.007
Thompson, J. M., Nuerk, H. C., Moeller, K., & Cohen Kadosh, R. (2013). The link between mental rotation ability and basic numerical representations. Acta Psychologica, 144(2), 324–331. https://doi.org/10.1016/j.actpsy.2013.05.009
Yazdani, S., Soluki, S., Arjmandnia, A. A., Fathabadi, J., Hassanzadeh, S., & Nejati, V. (2021). Spatial ability in children with Mathematics Learning Disorder (MLD) and its impact on executive functions. Developmental Neuropsychology, 46(3), 232–248. https://doi.org/10.1080/87565641.2021.1913165
Zhang, Xiao, & Rasanen, P. (2020). Early cognitive precursors of children’s mathematics learning disability and persistent low achievement: a 5-year longitudinal study. Child Development, 91(1), 7–27. https://doi.org/10.1111/cdev.13123
Zhang, Xiaoxian, Fu, W., Xue, L., Zhao, J., & Wang, Z. (2019). Children with mathematical learning difficulties are sluggish in disengaging attention. Frontiers in Psychology, 10(APR), 1–9. https://doi.org/10.3389/fpsyg.2019.00932
Beswick, K. (2008). Influencing teachers’ beliefs about teaching mathematics for numeracy to students with mathematics learning difficulties. Mathematics Teacher Education and Development, 9(2000), 3–20. http://ecite.utas.edu.au/55228/1/MTED_9_Beswick.pdf
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
Chinn, S. (2014). The routledge international handbook of dyscalculia and mathematical learning difficulties. In The Routledge International Handbook of Dyscalculia and Mathematical Learning Difficulties. https://doi.org/10.4324/9781315740713
Clements, D. H., Germeroth, C., & Sovran, B. (2015). The Building Blocks of Mathematics for Infants and Toddlers: An Annotated Bibliography for Course Developers 2015.
Creswell, J. W. (2014). Research design: Qualitative, quantitative, and mixed methods approaches. SAGE Publications. https://books.google.co.id/books?id=4uB76IC_pOQC
De Smedt, B., Taylor, J., Archibald, L., & Ansari, D. (2010). How is phonological processing related to individual differences in children’s arithmetic skills? Developmental Science, 13(3), 508–520. https://doi.org/10.1111/j.1467-7687.2009.00897.x
Dimitriu, D. G., & Dimitriu, D. C. (2020). A simple method to help students improve 3-D visualization skills. ASEE Annual Conference and Exposition, Conference Proceedings, 2020-June.
Dintarini, M., Jamil, A. F., & Ismail, A. D. (2022). Secondary students’ spatial thinking in solving the minimum competency assessment (MCA) on geometry. Jurnal Elemen, 8(2), 544–555. https://doi.org/10.29408/jel.v8i2.5670
Donnelly, E. L. H. (2021). Exploring the spatial-math link: The impact of tailored visual memory interventions for children with MLD. https://prism.ucalgary.ca/handle/1880/112974%0Ahttps://prism.ucalgary.ca/bitstream/handle/1880/112974/ucalgary_2021_donnelly_emma.pdf?sequence=2&isAllowed=y
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
Gunderson, E. A., Ramirez, G., Beilock, S. L., & Levine, S. C. (2012). The relation between spatial skill and early number knowledge: The role of the linear number line. Developmental Psychology, 48(5), 1229–1241. https://doi.org/10.1037/a0027433
Hamukwaya, S. T., & Haser, Ç. (2021). “It does not mean that they cannot do mathematics”: Beliefs about Mathematics Learning Difficulties. International Electronic Journal of Mathematics Education, 16(1), em0622. https://doi.org/10.29333/iejme/9569
Hasanah, U., & Kumoro, D. T. (2021). Kemampuan spasial: Kajian pada siswa usia sekolah dasar. Jurnal Pacu Pendidikan Dasar, 1(1), 27–34. https://unu-ntb.e-journal.id/pacu/article/view/68/19
Hawes, Z., Moss, J., Caswell, B., Naqvi, S., & MacKinnon, S. (2017). 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, 35(3), 236–264. https://doi.org/10.1080/07370008.2017.1323902
Karagiannakis, G., Baccaglini-frank, A., & Papadatos, Y. (2014). Mathematical learning difficulties subtypes classification. Frontiers in Human Neuroscience, 8(February), 1–5. https://doi.org/10.3389/fnhum.2014.00057
Khine, M. S. (2017). Visual-spatial ability in STEM education. In Visual-spatial Ability in STEM Education. https://doi.org/10.1007/978-3-319-44385-0
Kusuma, A. P., Rochmad, & Isnarto. (2021). Penerapan model accelerated learning cycle terhadap penalaran matematis ditinjau dari kemampuan spasial. PRISMA, Prosiding Seminar Nasional Matematika, 4(1), 75–79. https://journal.unnes.ac.id/sju/index.php/prisma/article/view/44952
Lestari, D. D. P., Budiarto, M. T., & Lukito, A. (2021). Analisis kemampuan spatial visualization siswa sekolah dasar dalam pemecahan masalah geometri: Ditinjau dari kemampuan matematika tingkat tinggi. ELSE (Elementary School Education Journal)?: Jurnal Pendidikan Dan Pembelajaran Sekolah Dasar, 5(1), 55. https://doi.org/10.30651/else.v5i1.7371
Levy, S., Turk-Browne, N. B., & Goldfarb, L. (2023). Impaired visuo-spatial statistical learning with mathematical learning difficulties. Visual Cognition, May. https://doi.org/10.1080/13506285.2023.2208887
Lowrie, T., Logan, T., Harris, D., & Hegarty, M. (2018). The impact of an intervention program on students’ spatial reasoning: student engagement through mathematics-enhanced learning activities. Cognitive Research: Principles and Implications, 3(1), 1–10. https://doi.org/10.1186/s41235-018-0147-y
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
Ma’rifatin, S., Amin, S. M., & Siswono, T. Y. E. (2019). Students’ mathematical ability and spatial reasoning in solving geometric problem. Journal of Physics: Conference Series, 1157(4). https://doi.org/10.1088/1742-6596/1157/4/042062
Mazzocco, M. M. M. (2009). An introduction to the special issue: Pathways to mathematical learning difficulties and disabilities. Developmental Disabilities Research Reviews, 15(1), 1–3. https://doi.org/10.1002/ddrr.52
Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative data analysis. SAGE Publications. https://books.google.co.id/books?id=3CNrUbTu6CsC
Murphy, M. M., Mazzocco, M. M. M., Hanich, L. B., & Early, M. C. (2007). Cognitive characteristics of children with mathematics learning disability (MLD) vary as a function of the cutoff criterion used to define MLD. Journal of Learning Disabilities, 40(5), 458–478.
Musriroh, R. Z., Hidayanto, E., & Rahardi, R. (2021). Penalaran spasial matematis dimensi persepsi dan visualisasi kelas VIII dalam pemecahan masalah geometri. Jurnal Pendidikan: Teori, Penelitian, Dan Pengembangan, 6(11), 1774. https://doi.org/10.17977/jptpp.v6i11.15144
Pavlovicova, G., & SvecovA, V. (2015). The development of spatial skills through discovering in the geometrical education at primary school. Procedia - Social and Behavioral Sciences, 186, 990–997. https://doi.org/10.1016/j.sbspro.2015.04.189
Pittalis, M., & Christou, C. (2010). Types of reasoning in 3D geometry thinking and their relation with spatial ability. Educational Studies in Mathematics, 75(2), 191–212. https://doi.org/10.1007/s10649-010-9251-8
Plerou, A., & Vlamos, P. (2016). Algorithmic thinking and mathematical learning difficulties classification. American Journal of Applied Psychology, 5(5), 22. https://doi.org/10.11648/j.ajap.20160505.11
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://doi.org/10.1177/0734282916659207
Skagerlund, K., & Träff, U. (2014). Development of magnitude processing in children with developmental dyscalculia: Space, time, and number. Frontiers in Psychology, 5(JUN), 1–16. https://doi.org/10.3389/fpsyg.2014.00675
Szucs, D., Devine, A., Soltesz, F., Nobes, A., & Gabriel, F. (2013). Developmental dyscalculia is related to visuo-spatial memory and inhibition impairment. Cortex, 49(10), 2674–2688. https://doi.org/10.1016/j.cortex.2013.06.007
Thompson, J. M., Nuerk, H. C., Moeller, K., & Cohen Kadosh, R. (2013). The link between mental rotation ability and basic numerical representations. Acta Psychologica, 144(2), 324–331. https://doi.org/10.1016/j.actpsy.2013.05.009
Yazdani, S., Soluki, S., Arjmandnia, A. A., Fathabadi, J., Hassanzadeh, S., & Nejati, V. (2021). Spatial ability in children with Mathematics Learning Disorder (MLD) and its impact on executive functions. Developmental Neuropsychology, 46(3), 232–248. https://doi.org/10.1080/87565641.2021.1913165
Zhang, Xiao, & Rasanen, P. (2020). Early cognitive precursors of children’s mathematics learning disability and persistent low achievement: a 5-year longitudinal study. Child Development, 91(1), 7–27. https://doi.org/10.1111/cdev.13123
Zhang, Xiaoxian, Fu, W., Xue, L., Zhao, J., & Wang, Z. (2019). Children with mathematical learning difficulties are sluggish in disengaging attention. Frontiers in Psychology, 10(APR), 1–9. https://doi.org/10.3389/fpsyg.2019.00932
Published
2024-05-17
How to Cite
AMALIA, Alfin Khoiro; AMIR, Mohammad Faizal.
Spatial Reasoning of Students With Mathematical Learning Difficulties.
Journal of Medives : Journal of Mathematics Education IKIP Veteran Semarang, [S.l.], v. 8, n. 2, p. 256 - 267, may 2024.
ISSN 2549-5070.
Available at: <https://e-journal.ivet.ac.id/index.php/matematika/article/view/3160>. Date accessed: 28 july 2025.
doi: https://doi.org/10.31331/medivesveteran.v8i2.3160.
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