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Educação e Ensino
Publicado: 2024-08-28

The contribution of working memory and spatial perception to the ability to solve geometric problems

Net Media Lab Mind - Brain R&D ΙΙΤ - N.C.S.R. "Demokritos" / Department of Primary Education, National and Kapodistrian University of Athens
Net Media Lab Mind - Brain R&D ΙΙΤ - N.C.S.R. "Demokritos"
Department of Primary Education, National and Kapodistrian University of Athens
Brain Functions, geometry, recognition, ageometria, Learning Difficulties, Working memory

Resumo

Geometry is a branch of mathematics that deals with the properties of space, including distance, shape, size, and the relative position of figures. It is one of the oldest branches of mathematics and has applications in various fields such as science, art, architecture, and even in areas seemingly unrelated to mathematics. Studies show that working memory and spatial perception contribute to students' geometry performance. This paper presents multiple studies demonstrating the brain regions activated when solving geometric problems. Interestingly, the brain areas activated when solving algebraic problems are different from those activated when solving geometric problems. Finally, multiple studies are presented that indicate students with learning difficulties lag in geometry, as solving geometric problems requires good reading and arithmetic skills.

Referências

  1. Allen, K., Giofrè, D., Higgins, S., & Adams, J. (2020). Working memory predictors of written mathematics in 7-to 8-year-old children. Quarterly Journal of Experimental Psychology, 73(2), 239–248.
  2. Anđelković, S., & Malinović-Jovanović, N. (2023). STUDENTS’ACHIEVEMENTS IN PRIMARY SCHOOL MATHEMATICS ACCORDING TO THE VAN HIELE MODEL OF THE DEVELOPMENT OF GEOMETRIC THINKING. Facta Universitatis, Series: Teaching, Learning and Teacher Education, 155–167.
  3. Angelopoulou, E., & Drigas, A. (2022). Working memory interventions via physical activity and ICTs: A strategic issue for the improvement of school students’ learning performance. Technium Soc. Sci. J., 30, 200.
  4. Angelopoulou, E., Karabatzaki, Z., & Drigas, A. (2021a). Assessing working memory in general education students for ADHD detection. Research, Society and Development, 10(10), e138101018766–e138101018766.
  5. Angelopoulou, E., Karabatzaki, Z., & Drigas, A. S. (2021b). The Role of Working Memory and Attention in Older Workers’ Learning. International Journal of Advanced Corporate Learning, 14(1).
  6. Armah, R. B., & Kissi, P. S. (2019). Use of the van hiele theory in investigating teaching strategies used by college of education geometry tutors. EURASIA Journal of Mathematics, Science and Technology Education, 15(4), em1694.
  7. Arnal-Bailera, A., & Manero, V. (2023). A characterization of van hiele’s level 5 of geometric reasoning using the delphi methodology. International Journal of Science and Mathematics Education, 1–24.
  8. Arsalidou, M., & Taylor, M. J. (2011). Is 2+ 2= 4? Meta-analyses of brain areas needed for numbers and calculations. Neuroimage, 54(3), 2382–2393.
  9. Bergstrom, C., & Zhang, D. (2016). Geometry interventions for K-12 students with and without disabilities: A research synthesis. International Journal of Educational Research, 80, 134–154.
  10. Bizzaro, M., Giofrè, D., Girelli, L., & Cornoldi, C. (2018a). Arithmetic, working memory, and visuospatial imagery abilities in children with poor geometric learning. Learning and Individual Differences, 62, 79–88.
  11. Bizzaro, M., Giofrè, D., Girelli, L., & Cornoldi, C. (2018b). Arithmetic, working memory, and visuospatial imagery abilities in children with poor geometric learning. Learning and Individual Differences, 62, 79–88.
  12. Blankenship, T. L., O’Neill, M., Ross, A., & Bell, M. A. (2015). Working memory and recollection contribute to academic achievement. Learning and Individual Differences, 43, 164–169.
  13. Bossé, M. J., Bayaga, A., Lynch-Davis, K., & DeMarte, A. (2021). Assessing analytic geometry understanding: Van Hiele, SOLO, and Beyond. International Journal for Mathematics Teaching and Learning, 22(1), 1–23.
  14. Brainin, E., Shamir, A., & Eden, S. (2021). Robot programming intervention for promoting spatial relations, mental rotation and visual memory of kindergarten children. Journal of Research on Technology in Education, 1–14.
  15. Brown, T., & Heywood, D. (2011). Geometry, subjectivity and the seduction of language: the regulation of spatial perception. Educational Studies in Mathematics, 77, 351–367.
  16. Bühner, M., Kröner, S., & Ziegler, M. (2008). Working memory, visual–spatial-intelligence and their relationship to problem-solving. Intelligence, 36(6), 672–680.
  17. Carretti, B., Borella, E., Cornoldi, C., & De Beni, R. (2009). Role of working memory in explaining the performance of individuals with specific reading comprehension difficulties: A meta-analysis. Learning and Individual Differences, 19(2), 246–251.
  18. Caviola, S., Mammarella, I. C., Cornoldi, C., & Lucangeli, D. (2012a). The involvement of working memory in children’s exact and approximate mental addition. Journal of Experimental Child Psychology, 112(2), 141–160.
  19. Caviola, S., Mammarella, I. C., Cornoldi, C., & Lucangeli, D. (2012b). The involvement of working memory in children’s exact and approximate mental addition. Journal of Experimental Child Psychology, 112(2), 141–160.
  20. Celik, H. S., & Yilmaz, G. K. (2022). Analysis of Van Hiele Geometric Thinking Levels Studies in Turkey: A Meta-Synthesis Study. International Journal of Curriculum and Instruction, 14(1), 473–501.
  21. Chaidi, E., Kefalis, C., Papagerasimou, Y., & Drigas, A. (2021). Educational robotics in Primary Education. A case in Greece. Research, Society and Development, 10(9), e17110916371–e17110916371.
  22. Chen, Y. H., Hsu, C. L., Wu, Y. J., Yi, Z., Wang, Y., & Thompson, D. R. (2023). Exploring attribute hierarchies of the van Hiele theory using diagnostic classification modeling and structural equation modeling.
  23. Clements, D. H. (2004). Geometric and spatial thinking in early childhood education. Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics Education, 267–297.
  24. de Oliveira, M. C. A., & Carneiro, R. F. (2022). Geometry Teaching in the Early Years: A History that Encourages Reflections on the Present. Acta Scientiae, 24(8), 537–566.
  25. Dorouka, P., Papadakis, S., & Kalogiannakis, M. (2020). Tablets and apps for promoting robotics, mathematics, STEM education and literacy in early childhood education. In Int. J. Mobile Learning and Organisation (Vol. 14, Issue 2).
  26. Doulou, A., Drigas, A., & Skianis, C. (2022). Mobile applications as intervention tools for children with ADHD for a sustainable education. Technium Sustainability, 2(4), 44–62.
  27. Drigas, A., Dede, D. E., & Dedes, S. (2020). Mobile and other applications for mental imagery to improve learning disabilities and mental health. International Journal of Computer Science Issues (IJCSI), 17(4), 18–23.
  28. Drigas, A., Ioannidou, R.-E., Kokkalia, G., & Lytras, M. D. (2014). ICTs, mobile learning and social media to enhance learning for attention difficulties. J. Univers. Comput. Sci., 20(10), 1499–1510.
  29. Drigas, A., Kokkalia, G., & Lytras, M. D. (2015a). ICT and collaborative co-learning in preschool children who face memory difficulties. Computers in Human Behavior, 51, 645–651.
  30. Drigas, A., Kokkalia, G., & Lytras, M. D. (2015b). Mobile and multimedia learning in preschool education. Journal of Mobile Multimedia, 119–133.
  31. Drigas, A., & Politi-Georgousi, S. (2019). Icts as a distinct detection approach for dyslexia screening: A contemporary view.
  32. 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.
  33. Ferreirós, J., & García-Pérez, M. J. (2020). Beyond natural geometry: on the nature of proto-geometry. Philosophical Psychology, 33(2), 181–205.
  34. Foley, J. M., Ribeiro-Filho, N. P., & Da Silva, J. A. (2004). Visual perception of extent and the geometry of visual space. Vision Research, 44(2), 147–156.
  35. Galitskaya, V., & Drigas, A. (2021). The importance of working memory in children with Dyscalculia and Ageometria. Scientific Electronic Archives, 14(10).
  36. Galitskaya, V., & Drigas, A. S. (2023). Mobiles & ICT Based Interventions for Learning Difficulties in Geometry. International Journal of Engineering Pedagogy, 13(4).
  37. Gallagher, A. M., & Kaufman, J. C. (2005). Gender Differences in Mathematics: What We Know and What We Need to Know. Cambridge University Press.
  38. Ganley, C. M., & Vasilyeva, M. (2014). The role of anxiety and working memory in gender differences in mathematics. Journal of Educational Psychology, 106(1), 105.
  39. García‐Madruga, J. A., Elosúa, M. R., Gil, L., Gómez‐Veiga, I., Vila, J. Ó., Orjales, I., Contreras, A., Rodríguez, R., Melero, M. Á., & Duque, G. (2013). Reading comprehension and working memory’s executive processes: An intervention study in primary school students. Reading Research Quarterly, 48(2), 155–174.
  40. Gathercole, S. E., Alloway, T. P., Willis, C., & Adams, A.-M. (2006). Working memory in children with reading disabilities. Journal of Experimental Child Psychology, 93(3), 265–281.
  41. Geary, D. C. (2003). Learning disabilities in arithmetic: Problem-solving differences and cognitive deficits. Handbook of Learning Disabilities, 199–212.
  42. Geary, D. C., Hoard, M. K., Byrd‐Craven, J., Nugent, L., & Numtee, C. (2007). Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child Development, 78(4), 1343–1359.
  43. Giofré, D., Mammarella, I. C., & Cornoldi, C. (2014). The relationship among geometry, working memory, and intelligence in children. Journal of Experimental Child Psychology, 123, 112–128.
  44. Giofrè, D., Mammarella, I. C., Ronconi, L., & Cornoldi, C. (2013a). Visuospatial working memory in intuitive geometry, and in academic achievement in geometry. Learning and Individual Differences, 23(1), 114–122. https://doi.org/10.1016/j.lindif.2012.09.012
  45. Giofrè, D., Mammarella, I. C., Ronconi, L., & Cornoldi, C. (2013b). Visuospatial working memory in intuitive geometry, and in academic achievement in geometry. Learning and Individual Differences, 23(1), 114–122. https://doi.org/10.1016/j.lindif.2012.09.012
  46. Gonsalves, N., & Krawec, J. (2014). Using number lines to solve math word problems: A strategy for students with learning disabilities. Learning Disabilities Research & Practice, 29(4), 160–170.
  47. González, A., Gavilán-Izquierdo, J. M., Gallego-Sánchez, I., & Puertas, M. L. (2022). A Theoretical Analysis of the Validity of the Van Hiele Levels of Reasoning in Graph Theory. Journal on Mathematics Education, 13(3), 515–530.
  48. Hambrick, D. Z., Libarkin, J. C., Petcovic, H. L., Baker, K. M., Elkins, J., Callahan, C. N., Turner, S. P., Rench, T. A., & LaDue, N. D. (2012). A test of the circumvention-of-limits hypothesis in scientific problem solving: the case of geological bedrock mapping. Journal of Experimental Psychology: General, 141(3), 397.
  49. Hannafin, R. D., Truxaw, M. P., Vermillion, J. R., & Liu, Y. (2008). Effects of spatial ability and instructional program on geometry achievement. The Journal of Educational Research, 101(3), 148–157.
  50. Hansen, V. L. (1998). General considerations on curricula designs in geometry. NEW ICMI STUDIES SERIES, 5, 235–242.
  51. Hassan, M. N., Abdullah, A. H., & Ismail, N. (2020a). Effects of Integrative Interventions With Van Hiele Phase on Students’ Geometric Thinking: a Systematic Review. Journal of Critical Reviews, 7(13), 1133–1140.
  52. Hassan, M. N., Abdullah, A. H., & Ismail, N. (2020b). Effects of VH-iSTEM Learning Strategy on Basic Secondary School Students’ Degree of Acquisition of van Hiele Levels of Thinking in Sokoto State, Nigeria. Universal Journal of Educational Research, 8(9), 4213–4223.
  53. Hatfield, G. (1984). Spatial perception and geometry in Kant and Helmholtz. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 1984(2), 568–587.
  54. Heathcote, D. (1994). The role of visuo-spatial working memory in the mental addition of multi-digit addends. Cahiers de Psychologie Cognitive/Current Psychology of Cognition.
  55. Hsi, S., Linn, M. C., & Bell, J. E. (1997). The role of spatial reasoning in engineering and the design of spatial instruction. Journal of Engineering Education, 86(2), 151–158.
  56. Izard, V., Pica, P., Spelke, E. S., & Dehaene, S. (2011). Flexible intuitions of Euclidean geometry in an Amazonian indigene group. Proceedings of the National Academy of Sciences of the United States of America, 108(24), 9782–9787. https://doi.org/10.1073/pnas.1016686108
  57. Izard, V., & Spelke, E. S. (2009). Development of Sensitivity to Geometry in Visual Forms. Human Evolution, 23(3), 213–248.
  58. Jumadi, A., Nasrudin, F. S. M., Arunah, N. S. K., Mohammad, S. A., Abd Ghafar, N., & Zainuddin, N. A. (2022). Students’ and Lecturers’ Perceptions of Students’ Difficulties in Geometry Courses. International Journal of Advanced Research in Education and Society, 4(2), 50–64.
  59. Juman, Z. A. M. S., Mathavan, M., Ambegedara, A. S., & Udagedara, I. G. K. (2022a). Difficulties in Learning Geometry Component in Mathematics and Active-Based Learning Methods to Overcome the Difficulties. Shanlax International Journal of Education, 10(2), 41–58.
  60. Juman, Z. A. M. S., Mathavan, M., Ambegedara, A. S., & Udagedara, I. G. K. (2022b). Difficulties in Learning Geometry Component in Mathematics and Active-Based Learning Methods to Overcome the Difficulties. Shanlax International Journal of Education, 10(2), 41–58.
  61. Kao, Y. S., Douglass, S. A., M Fincham, J., & R Anderson, J. (2008). Traveling the second bridge: Using fMRI to assess an ACT-R model of geometry proof.
  62. Kefalis, C., Kontostavlou, E.-Z., & Drigas, A. (2020). The Effects of Video Games in Memory and Attention. Int. J. Eng. Pedagog., 10(1), 51–61.
  63. Kokkalia, G., Drigas, A. S., & Economou, A. (2016). Mobile learning for preschool education. International Journal of Interactive Mobile Technologies, 10(4).
  64. Kokkalia, G. K., & Drigas, A. S. (2015). Working Memory and ADHD in Preschool Education. The Role of ICT’S as a Diagnostic and Intervention Tool: An Overview. International Journal of Emerging Technologies in Learning, 10(5).
  65. Krawec, J. L. (2014). Problem representation and mathematical problem solving of students of varying math ability. Journal of Learning Disabilities, 47(2), 103–115.
  66. Kusuma, M. A., Yuliati, N., Maharani, P., & Hasanah, N. (2021). Thinking process of 7th class students in understanding quadrilateral concepts based on Van Hiele theory. Journal of Physics: Conference Series, 1839(1), 012012.
  67. Kyttälä, M., & Lehto, J. E. (2008). Some factors underlying mathematical performance: The role of visuospatial working memory and non-verbal intelligence. European Journal of Psychology of Education, 23, 77–94.
  68. Leikin, M., Waisman, I., Shaul, S., & Leikin, R. (2014). Brain activity associated with translation from a visual to a symbolic representation in algebra and geometry. Journal of Integrative Neuroscience, 13(01), 35–59.
  69. Li, Y., & Geary, D. C. (2013). Developmental gains in visuospatial memory predict gains in mathematics achievement. PloS One, 8(7), e70160.
  70. Liapi, K. A. (2002). Geometry in architectural engineering education revisited. Journal of Architectural Engineering, 8(3), 80–88.
  71. Linde-Domingo, J., & Spitzer, B. (2022). Geometry of visual working memory information in human gaze patterns. BioRxiv, 2011–2022.
  72. Lumbre, A. P., Beltran-Joaquin, M. N., & Monterola, S. L. C. (2023). Relationship between mathematics teachers’ van Hiele levels and students’ achievement in geometry. International Journal of Studies in Education and Science (IJSES), 4(2), 113–123.
  73. Ma, H.-L., Lee, D.-C., Lin, S.-H., & Wu, D.-B. (2015). A study of van Hiele of geometric thinking among 1st through 6th graders. Eurasia Journal of Mathematics, Science and Technology Education, 11(5), 1181–1196.
  74. 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), ep21007.
  75. Mahlaba, S. C., & Mudaly, V. (2022). Exploring the relationship between commognition and the Van Hiele theory for studying problem-solving discourse in Euclidean geometry education. Pythagoras, 43(1), 1–11.
  76. Maier, P. H. (1996). Spatial geometry and spatial ability–How to make solid geometry solid. Selected Papers from the Annual Conference of Didactics of Mathematics, 63–75.
  77. Mammarella, I. C., Giofrè, D., Ferrara, R., & Cornoldi, C. (2013). Intuitive geometry and visuospatial working memory in children showing symptoms of nonverbal learning disabilities. Child Neuropsychology, 19(3), 235–249.
  78. Moru, E. K., Malebanye, M., Morobe, N., & George, M. J. (2021a). A Van Hiele Theory Analysis for Teaching Volume of Three-Dimensional Geometric Shapes. Journal of Research and Advances in Mathematics Education, 6(1), 17–31.
  79. Moser-Mercer, B. (2023). Working memory in simultaneous and consecutive interpreting. In The Routledge Handbook of Translation, Interpreting and Bilingualism (pp. 129–144). Routledge.
  80. Naufal, M. A., Abdullah, A. H., Osman, S., Abu, M. S., & Ihsan, H. (2020b). Van hiele level of geometric thinking among secondary school students. International Journal of Recent Technology and Engineering (IJRTE), 8(6), 478–481.
  81. Naufal, M. A., Abdullah, A. H., Osman, S., Abu, M. S., & Ihsan, H. (2021a). Reviewing the Van Hiele Model and the Application of Metacognition on Geometric Thinking. International Journal of Evaluation and Research in Education, 10(2), 597–605.
  82. Naufal, M. A., Abdullah, A. H., Osman, S., Abu, M. S., & Ihsan, H. (2021b). The Effectiveness of Infusion of Metacognition in van Hiele Model on Secondary School Students’ Geometry Thinking Level. International Journal of Instruction, 14(3), 535–546.
  83. Neubrand, M. (1998). General tendencies in the development of geometry teaching in the past two decades. Perspectives on the Teaching of Geometry for the 21st Century, 226–228.
  84. Newcombe, N. S., Booth, J. L., & Gunderson, E. A. (2019). Spatial skills, reasoning, and mathematics. In The Cambridge Handbook of Cognition and Education (pp. 100–123). Cambridge University Press. https://doi.org/10.1017/9781108235631.006
  85. Newman, S. D., Willoughby, G., & Pruce, B. (2011). The effect of problem structure on problem-solving: an fMRI study of word versus number problems. Brain Research, 1410, 77–88.
  86. Nordvik, H., & Amponsah, B. (1998). Gender differences in spatial abilities and spatial activity among university students in an egalitarian educational system. Sex Roles, 38(11), 1009–1023.
  87. Owens, K., & Outhred, L. (2006). The complexity of learning geometry and measurement. In Handbook of research on the psychology of mathematics education (pp. 83–115). Brill.
  88. Pappas, M. A., Drigas, A. S., & Polychroni, F. (2018). An eight-layer model for mathematical cognition. International Journal of Emerging Technologies in Learning (Online), 13(10), 69.
  89. Passolunghi, M. C., Lanfranchi, S., Altoè, G., & Sollazzo, N. (2015). Early numerical abilities and cognitive skills in kindergarten children. Journal of Experimental Child Psychology, 135, 25–42.
  90. Passolunghi, M. C., & Mammarella, I. C. (2010). Spatial and visual working memory ability in children with difficulties in arithmetic word problem solving. European Journal of Cognitive Psychology, 22(6), 944–963.
  91. Passolunghi, M. C., & Mammarella, I. C. (2012). Selective spatial working memory impairment in a group of children with mathematics learning disabilities and poor problem-solving skills. Journal of Learning Disabilities, 45(4), 341–350.
  92. Passolunghi, M. C., Mammarella, I. C., & Altoè, G. (2008). Cognitive abilities as precursors of the early acquisition of mathematical skills during first through second grades. Developmental Neuropsychology, 33(3), 229–250.
  93. Pelegrina, S., Capodieci, A., Carretti, B., & Cornoldi, C. (2015). Magnitude representation and working memory updating in children with arithmetic and reading comprehension disabilities. Journal of Learning Disabilities, 48(6), 658–668.
  94. Peng, P., & Fuchs, D. (2016). A Meta-Analysis of Working Memory Deficits in Children With Learning Difficulties: Is There a Difference Between Verbal Domain and Numerical Domain? Journal of Learning Disabilities, 49(1), 3–20. https://doi.org/10.1177/0022219414521667
  95. Poletti, M. (2016). WISC-IV intellectual profiles in Italian children with specific learning disorder and related impairments in reading, written expression, and mathematics. Journal of Learning Disabilities, 49(3), 320–335.
  96. Pujawan, I., Suryawan, I., & Prabawati, D. A. A. (2020). The Effect of Van Hiele Learning Model on Students’ Spatial Abilities. International Journal of Instruction, 13(3), 461–474.
  97. Rivella, C., Cornoldi, C., Caviola, S., & Giofrè, D. (2021). Learning a new geometric concept: The role of working memory and of domain‐specific abilities. British Journal of Educational Psychology, 91(4), 1537–1554.
  98. Roldán-Zafra, J., Perea, C., Polo Blanco, I., & Campillo, P. (2022). Design of an interactive module based on the van hiele model: case study of the Pythagorean Theorem.
  99. Segerby, C. (2023). Linguistic Challenges in Geometry: Making the Mathematical Content Accessible to Include All Students. In Developing Inclusive Environments in Education: Global Practices and Curricula (pp. 229–254). IGI Global.
  100. Senk, S. L., Thompson, D. R., Chen, Y. H., Voogt, K., & Usiskin, Z. (2022). The van Hiele Geometry Test: History, use, and suggestions for revisions. University of Chicago School Mathematics Project.
  101. Siquara, G. M., dos Santos Lima, C., & Abreu, N. (2018). Working memory and intelligence quotient: Which best predicts on school achievement? Psico, 49(4), 365–374.
  102. Sisman, B., Kucuk, S., & Yaman, Y. (2021). The effects of robotics training on children’s spatial ability and attitude toward STEM. International Journal of Social Robotics, 13(2), 379–389.
  103. Skiada, R., Soroniati, E., Gardeli, A., & Zissis, D. (2014). EasyLexia: A Mobile Application for Children with Learning Difficulties. Procedia Computer Science, 27, 218–228.
  104. Stathopoulou, A., Karabatzaki, Z., Tsiros, D., Katsantoni, S., & Drigas, A. (2019). Mobile apps the educational solution for autistic students in secondary education.
  105. Stathopoulou, A., Loukeris, D., Karabatzaki, Z., Politi, E., Salapata, Y., & Drigas, A. (2020). Evaluation of mobile apps effectiveness in children with autism social training via digital social stories.
  106. Swanson, H. L., & Beebe-Frankenberger, M. (2004). The relationship between working memory and mathematical problem solving in children at risk and not at risk for serious math difficulties. Journal of Educational Psychology, 96(3), 471.
  107. Swanson, H. L., & Fung, W. (2016). Working memory components and problem-solving accuracy: Are there multiple pathways? Journal of Educational Psychology, 108(8), 1153.
  108. Swanson, H. L., & Jerman, O. (2006). Math disabilities: A selective meta-analysis of the literature. Review of Educational Research, 76(2), 249–274.
  109. Swanson, H. L., Zheng, X., & Jerman, O. (2009). Working memory, short-term memory, and reading disabilities: A selective meta-analysis of the literature. Journal of Learning Disabilities, 42(3), 260–287.
  110. 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.
  111. Usiskin, Z., & Senk, S. (1990). Evaluating a test of van Hiele levels: A response to Crowley and Wilson. Journal for Research in Mathematics Education, 21(3), 242–245.
  112. Utomo, D. P., Amaliyah, T. Z., Darmayanti, R., Usmiyatun, U., & Choirudin, C. (2023a). Students’ Intuitive Thinking Process in Solving Geometry Tasks from the Van Hiele Level. JTAM (Jurnal Teori Dan Aplikasi Matematika), 7(1), 139–149.
  113. Utomo, D. P., Amaliyah, T. Z., Darmayanti, R., Usmiyatun, U., & Choirudin, C. (2023b). Students’ Intuitive Thinking Process in Solving Geometry Tasks from the Van Hiele Level. JTAM (Jurnal Teori Dan Aplikasi Matematika), 7(1), 139–149.
  114. UYGUN, T., & GÜNER, P. (2021). Van Hiele Levels of Geometric Thinking and Constructivist-Based Teaching Practices. Mersin Üniversitesi Eğitim Fakültesi Dergisi, 17(1), 22–40.
  115. Van de Weijer-Bergsma, E., Kroesbergen, E. H., & Van Luit, J. E. H. (2015). Verbal and visual-spatial working memory and mathematical ability in different domains throughout primary school. Memory & Cognition, 43, 367–378.
  116. Van Garderen, D., & Montague, M. (2003b). Visual–spatial representation, mathematical problem solving, and students of varying abilities. Learning Disabilities Research & Practice, 18(4), 246–254.
  117. Voyer, D., Voyer, S. D., & Saint-Aubin, J. (2017). Sex differences in visual-spatial working memory: A meta-analysis. Psychonomic Bulletin & Review, 24, 307–334.
  118. Wagner, M. (2008). Comparing the psychophysical and geometric characteristics of spatial perception and cognitive maps. Cognitive Studies: Bulletin of the Japanese Cognitive Science Society, 15(1), 6–21.
  119. Wahyuni, A., Effendi, L. A., Angraini, L. M., & Andrian, D. (2020). Developing instrument to increase students’ geometry ability based on Van Hiele level integrated with Riau Malay culture. Jurnal Penelitian Dan Evaluasi Pendidikan, 24(2), 208–217.
  120. Wai, J., Lubinski, D., Benbow, C. P., & Steiger, J. H. (2010). Accomplishment in science, technology, engineering, and mathematics (STEM) and its relation to STEM educational dose: A 25-year longitudinal study. Journal of Educational Psychology, 102(4), 860.
  121. Xie, Y., Hu, P., Li, J., Chen, J., Song, W., Wang, X.-J., Yang, T., Dehaene, S., Tang, S., & Min, B. (2022). Geometry of sequence working memory in macaque prefrontal cortex. Science, 375(6581), 632–639.
  122. Zacks, J. M. (2008). Neuroimaging studies of mental rotation: a meta-analysis and review. Journal of Cognitive Neuroscience, 20(1), 1–19.
  123. Zavitsanou, A. M., & Drigas, A. (2021). Attention and Working Memory. Int. J. Recent Contributions Eng. Sci. IT, 9(1), 81–91.
  124. Zhang, D. (2017). Effects of visual working memory training and direct instruction on geometry problem solving in students with geometry difficulties. Learning Disabilities: A Contemporary Journal, 15(1), 117–138.
  125. Zhang, D., Ding, Y., Stegall, J., & Mo, L. (2012). The effect of visual‐chunking‐representation accommodation on geometry testing for students with math disabilities. Learning Disabilities Research & Practice, 27(4), 167–177.
  126. Zheng, X., Swanson, H. L., & Marcoulides, G. A. (2011). Working memory components as predictors of children’s mathematical word problem solving. Journal of Experimental Child Psychology, 110(4), 481–498.
  127. Zhou, L., Liu, J., & Lo, J.-J. (2022). A comparison of US and Chinese geometry standards through the lens of van Hiele levels. International Journal of Education in Mathematics, Science and Technology, 10(1), 38–56.

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Galitskaya, V., Drigas, A., & Antoniou Α.-S. (2024). The contribution of working memory and spatial perception to the ability to solve geometric problems. Scientific Electronic Archives, 17(5). https://doi.org/10.36560/17520241973