Journal of Research in Science, Mathematics and Technology Education

Defining Spatial Reasoning: A Content Analysis to Explicate Spatial Reasoning Skills for Early Childhood Educators’ Use

Journal of Research in Science, Mathematics and Technology Education, Volume 7, Issue SI, June 2024, pp. 141-176
OPEN ACCESS VIEWS: 524 DOWNLOADS: 496 Publication date: 15 Jun 2024
ABSTRACT
Spatial reasoning is critical for mathematics learning and achievement, and its comprising skills are necessary in science, technology, engineering, and mathematics careers. To support young children in learning to reason spatially, clear definitions of the construct and supports for early childhood educators to teach the skills are needed. This study defines spatial reasoning as a comprehensive, comprehensible framework of skills. Using problem-driven content analysis, 835 text units from 103 sources, plus definitions from two reputable dictionary sources, were used to adopt, adapt, and infer the definitions for 40 terms that collectively represent spatial reasoning. Findings provide both the definitions and evidence of the extent to which various spatial reasoning skills have been investigated empirically. Directions for future research are discussed, including the need to refine the framework to ensure its utility for teachers and researchers.
KEYWORDS
Spatial Reasoning, Content Analysis, Mathematics Education, Early Childhood Education
CITATION (APA)
Pinilla, R. K. (2024). Defining Spatial Reasoning: A Content Analysis to Explicate Spatial Reasoning Skills for Early Childhood Educators’ Use. Journal of Research in Science, Mathematics and Technology Education, 7(SI), 141-176. https://doi.org/10.31756/jrsmte.317SI
REFERENCES
  1. (* indicate sources directly informing skill definitions; see Appendices B and C. indicate sources collected but not included in the definitions; see Appendix B only)
  2. Amorim, M.-A., Isableu, B., & Jarraya, M. (2006). Embodied spatial transformations: “Body analogy” for the mental rotation of objects. Journal of Experimental Psychology: General, 135(3), 327–347. https://doi.org/10.1037/0096-3445.135.3.327
  3. Anooshian, L. J., Pascal, V. U., & McCreath, H. (1984). Problem mapping before problem solving: Young children’s cognitive maps and search strategies in large-scale environments. Child Development, 55(5), 1820–1834. https://doi.org/10.2307/1129929
  4. *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
  5. *Battista, M. T., Clements, D. H., Arnoff, J., Battista, K., & Borrow, C. V. A. (1998). Students’ spatial structuring of 2D arrays of squares. Journal for Research in Mathematics Education, 29(5), 503–532. https://doi.org/10.5951/jresematheduc.29.5.0503
  6. *Bertenthal, B. I., Campos, J. J., & Kermoian, R. (1994). An epigenetic perspective on the development of self-produced locomotion and its consequences. Current Directions in Psychological Sciences, 3(5), 140–145. https://doi.org/10.1111/1467-8721.ep10770621
  7. Blaut, J. M., & Stea, D. (1974). Mapping at the age of three. Journal of Geography, 73(7), 5–9. https://doi.org/10.1080/00221347408980311
  8. *Blades, M., Spencer, C., Plester, B., & Desmond, K. (2004). Young children’s recognition and representation of urban landscapes: From aerial photographs and in toy play. In G. L. Allen (Ed.), Human spatial memory: Remembering where (pp. 287–308). Lawrence Erlbaum Associates. https://doi.org/10.4324/9781410609984
  9. Boardman, D. (1990). Graphicacy revisited: Mapping abilities and gender differences. Educational Review, 42(1), 57–64. https://doi.org/10.1080/0013191900420106
  10. Boykin, W., & Noguera, P. A. (2011). Creating the opportunity to learn: Moving from research to practice to close the achievement gap. Association for Supervision and Curriculum Development.
  11. *Bremner, J. G., & Taylor, A. J. (1982). Children’s errors in copying angles: Perpendicular error or bisection error? Perception, 11(2), 163–171. https://doi.org/10.1068/p110163
  12. Brosnan, M. J. (1998). Spatial ability in children’s play with Lego blocks. Perceptual and Motor Skills, 87(1), 19–28. https://doi.org/10.2466/pms.1998.87.1.19
  13. Bruce, C. D., Davis, B., Sinclair, N., McGarvey, L., Hallowell, D., Drefs, M., Francis, K., Hawes, Z., Moss, J., Mulligan, J., Okamoto, Y., Whiteley, W., & Woolcott, G. (2017). Understanding gaps in research networks: Using “spatial reasoning” as a window into the importance of networked educational research. Educational Studies in Mathematics, 95, 143–161. https://doi.org/10.1007/s10649-016-9743-2
  14. *Bryant, P. E. (2008). Paper 5: Understanding spaces and its representation in mathematics. Nuffield Foundation. https://www.nuffieldfoundation.org/wp-content/uploads/2019/12/P5.pdf
  15. *Bushnell, E. W., McKenzie, B. E., Lawrence, D. A., & Com, S. (1995). The spatial coding strategies of 1-year-old infants in a locomotor search task. Child Development, 66(4), 937–958. https://doi.org/10.2307/1131790
  16. *Caldera, Y. M., Culp, A. M., O’Brien, M., Truglio, R. T., Alvarez, M., & Huston, A. C. (1999). Children’s play preferences, construction play with blocks, and visual-spatial skills: Are they related? International Journal of Behavioral Development, 23(4), 855–872. https://doi.org/10.1080/016502599383577
  17. Cariglia-Bull, T., & Pressley, M. (1990). Short-term memory differences between children predict imagery effects when sentences are read. Journal of Experimental Child Psychology. 49(3), 384–398. https://doi.org/10.1016/0022-0965(90)90066-h
  18. Case, R., Stephenson, K. M., Bleiker, C., & Okamoto, Y. (1996). Central spatial structures and their development. In R. Case & Y. Okamoto (Eds.), The role of central conceptual structures in the development of children’s thought. Monographs of the Society for Research in Child Development, 61(1–2), 83–102. https://doi.org/ 10.1111/j.1540-5834.1996.tb00539.x
  19. *Casey, B., Andrews, N., Schindler, H., Kersh, J. E., Samper, A., & Copley, J. (2008). The development of spatial skills through interventions involving block building activities. Cognition and Instruction, 26(3), 269–309. https://doi.org/10.1080/07370000802177177
  20. Casey, B., Erkut, S., Ceder, I., & Young, J. (2008). Use of a storytelling context to improve girls’ and boys’ geometry skills in kindergarten. Journal of Applied Developmental Psychology, 29(1), 29–48. https://doi.org/10.1016/j.appdev.2007.10.005
  21. Casey, B. M., & Fell, H. (2018). Spatial reasoning: A critical problem-solving tool in children’s mathematics strategy tool-kit. In K. Mix & M. Battista (Eds.), Visualizing mathematics: The role of spatial reasoning in mathematical thought (pp. 47–75). Springer. https://doi.org/10.1007/978-3-319-98767-5
  22. *Chase, W. G., & H. A. Simon. (1973). Perception in chess. Cognitive Psychology 4(1), 55–81. https://doi.org/10.1016/0010-0285(73)90004-2
  23. Cheng, K., Huttenlocher, J., & Newcombe, N. S. (2013). 25 years of research on the use of geometry in spatial reorientation: A current theoretical perspective. Psychonomic Bulletin & Review, 20(6), 1033-1052. https://doi.org/10.3758/s13423-013-0416-1
  24. *Chu, M., & Kita, S. (2011). The nature of gestures’ beneficial role in spatial problem solving. Journal of Experimental Psychology: General, 140(1), 102–116. https://doi.org/10.1037/a0021790
  25. Clements, D. H. (2004a). Geometric and spatial thinking in early childhood education. In D. H. Clements, J. Sarama & A.-M. DiBiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 267–297). Lawrence Erlbaum Associates. https://doi.org/10.4324/9781410609236
  26. Clements, D. H. (2004b). Perspective on “The Child’s Thought and Geometry.” In T. P. Carpenter, J. A. Dossey, & J. L. Koehler (Eds.)., Classics in mathematics education research (p. 60). National Council of Teachers of Mathematics.
  27. *Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420–464). Macmillan.
  28. Clements, D. H., Battista, M. T., Sarama, J., & Swaminathan, S. (1996). Development of turn and turn measurement concepts in a computer-based instructional unit. Educational Studies in Mathematics, 30, 313–337. https://doi.org/10.1007/BF00570828
  29. Clements, D. H., & Burns, B. A. (2000). Students’ development of strategies for turn and angle measure. Educational Studies in Mathematics, 41, 31–45. https://doi.org/10.1023/A:1003938415559
  30. Clements, D. H., & Sarama, J. (2007). Building blocks—SRA real math, Grade PreK. SRA/McGraw-Hill.
  31. Clements, D. H., & Sarama, J. (2011). Early childhood teacher education: The case of geometry. Journal of Mathematics Teacher Education, 14(2), 133–148. https://doi.org/10.1007/s10857-011-9173-0
  32. *Clements, D. H., Swaminathan, S., Hannibal, M. A. Z., & Sarama, J. (1999). Young children’s concepts of shape. Journal for Research in Mathematics Education, 30(2), 192–212. https://doi.org/10.2307/749610
  33. Confrey, J., Maloney, A. P., & Corley, A. K. (2014). Learning trajectories: A framework for connecting standards with curriculum. ZDM: The International Journal on Mathematics Education, 46, 719–733. https://doi.org/10.1007/s11858-014-0598-7
  34. Copley, J. V. (2010). The young child and mathematics (2nd ed.). National Association for the Education of Young Children.
  35. Creswell, J. W., & Poth, C. N. (2018). Qualitative inquiry & research design: Choosing among the five approaches (4th ed.). Sage.
  36. Dalke, D. E. (1998). Charting the development of representational skills: When do children know that maps can lead and mislead? Cognitive Development, 13(1), 53–72. https://doi.org/10.1016/S0885-2014(98)90020-X
  37. *Davis, B., & Spatial Reasoning Study Group. (Eds.). (2015). Spatial reasoning in the early years: Principles, assertions, and speculations. Routledge. https://doi.org/10.4324/9781315762371
  38. Dehaene, S., Izard, V., Pica, P., & Spelke, E. S. (2006). Core knowledge of geometry in an Amazonian Indigene group. Science, 311(5759), 381–384. https://doi.org/10.1126/science.1121739
  39. *DeLoache, J. S. (1987). Rapid change in the symbolic functioning of young children. Science, 238(4833), 1556–1557. https://doi.org/10.1126/science.2446392
  40. DeLoache, J. S., & Burns, N. M. (1994). Early understanding of the representational function of pictures. Cognition, 52(2), 83–110. https://doi.org/10.1016/0010-0277(94)90063-9
  41. Denzin, N. K., & Lincoln, Y. S. (Eds.). (2000). Handbook of qualitative research (2nd ed., pp. 1–28). Sage.
  42. Duschl, R., Maeng, S., & Sezen, A. (2011). Learning progressions and teaching sequences: A review and analysis. Studies in Science Education, 47(2), 123–182. https://doi.org/10.1080/03057267.2011.604476
  43. *Edwards, L. D. (1991). Children’s learning in a computer microworld for transformation geometry. Journal for Research in Mathematics Education, 22(2), 122–137. https://doi.org/10.2307/749589
  44. Ehrlich, S. B., Levine, S. C., & Goldin-Meadow, S. (2006). The importance of gesture in children’s spatial reasoning. Developmental Psychology, 42(6), 1259–1268. https://doi.org/10.1037/0012-1649.42.6.1259
  45. *Empson, S. B., & Turner, E. (2006). The emergence of multiplicative thinking in children’s solutions to paper folding tasks. The Journal of Mathematical Behavior, 25(1), 46–56. https://doi.org/10.1016/j.jmathb.2005.11.001
  46. Franklin, N., and B. Tversky. 1990. Searching imagined environments. Journal of Experimental Psychology: General, 119(1), 63–76. https://doi.org/10.1037/0096-3445.119.1.63
  47. *French, J. W., Ekstrom, R. B., & Price, L. A. (1963). Manual for kit of reference tests for cognitive factors, revised edition. Educational Testing Service. https://apps.dtic.mil/sti/pdfs/AD0410915.pdf
  48. *Frick, A., & Newcombe, N. S. (2012). Getting the big picture: Development of spatial scaling abilities. Cognitive Development, 27(3), 270–282. https://doi.org/10.1016/j.cogdev.2012.05.004
  49. Fuys, D., Geddes, D., & Tischler, R. (1984). English translation of selected writings of Dina van Hiele-Geldof and Pierre M. van Hiele. Brooklyn College. https://eric.ed.gov/?id=EJ1289441
  50. Geary, D. C., Saults, S. J., Liu, F., & Hoard, M. K. (2000). Sex differences in spatial cognition, computational fluency, and arithmetical reasoning. Journal of Experimental Child Psychology, 77(4), 337–353. https://doi.org/10.1006/jecp.2000.2594
  51. Gilligan-Lee, K. A., Hawes, Z. C. K., & Mix, K. S. (2022). Spatial thinking as the missing piece in mathematics curricula. npj Science of Learning, 7, Article 10. https://doi.org/10.1038/s41539-022-00128-9
  52. Ginsburg, H. P., Kaplan, R, G., Cannon, J., Cordero, M. I., Eisenband, J. G., Galanter, M., & Morgenlander, M. (2006). Helping early childhood educators to teach mathematics. In M. Zaxlow & I. Martinez-Beck (Eds.), Critical issues in early childhood professional development (pp. 171–202). Paul H. Brookes Publishing Co.
  53. Glaser, B. G., & Strauss, A. L. (1967). The discovery of grounded theory. Aldine.
  54. Goodson, B. D. (1982). The development of hierarchic organization: The reproduction, planning, and perception of multiarch block structures. In G. E. Forman (Ed.), Action and thought (pp. 165–201). Academic Press.
  55. Greenough, W. T., Black, J. E., & Wallace, C. S. (1987). Experience and brain development. Child Development, 58(3), 539–559. https://doi.org/10.2307/1130197
  56. Guay, R. B., & McDaniel, E. D. (1977). The relationship between mathematics achievement and spatial abilities among elementary school children. Journal for Research in Mathematics Education, 8(3), 211–215. https://doi.org/10.2307/748522
  57. Gunderson, E. A., Ramirez, G., Beilock, S. L., & Levine, S. C. (2012). The relation between spatial skills and early number knowledge: The role of the linear number line. Developmental Psychology,48(5), 1229–1241. https://doi.org/ 10.1037/a0027433
  58. Hallowell, D. A., Okamoto, Y., Romo, L. F., & La Joy, J. R. (2015). First-grader’s spatial-mathematical reasoning about plane and solid shapes and their representations. ZDM: The International Journal on Mathematics Education, 47, 363-375. https://doi.org/10.1007/s11858-015-0664-9
  59. Hanson, S., & Hanson, P. (1993). The geography of everyday life. In T. Gärling & R. G. Golledge (Eds.), Behavior and environment (pp. 249–269). Elsevier Science Publishers.
  60. Hawes, Z., & Ansari, D. (2020). What explains the relationship between spatial and mathematical skills? A review of evidence from brain and behavior. Psychonomic Bulletin & Review, 27(3), 465–482. https://doi.org/10.3758/s13423-019-01694-7
  61. 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
  62. *Hegarty, M., & Just, M. A. (1993). Constructing mental models of machines from text and diagrams. Journal of Memory and Language, 32(6), 717–742. https://doi.org/10.1006/jmla.1993.1036
  63. *Hegarty, M., & Waller, D. A. (2005). Individual differences in spatial abilities. In P. Shah & A. Miyake (Eds.), Handbook of visuospatial thinking (pp. 121–169). Cambridge University Press. https://doi/10.1017/CBO9780511610448.005
  64. *Heiser, J., & Tversky, B. (2002). Diagrams and descriptions in acquiring complex systems. In W. Gray & C. Schunn (Eds.), Proceedings of the Cognitive Science Society meetings (pp. 447–452). Erlbaum Associates.
  65. Henderson, D. W., & Taimina, D. (2005). Experiencing geometry: Euclidean and non-Euclidean with history. Prentice Hall.
  66. *Huttenlocher, J., Newcombe, N. S., & Vasilyeva, M. (1999). Spatial scaling in young children. Psychological Science, 10(5), 393–398. https://doi.org/10.1111/1467-9280.00175
  67. Jauåovec, N., & Jauåovec, K. (2012). Sex differences in mental rotation and cortical activation patterns: Can training change them? Intelligence, 40(2), 151–162. https://doi.org/10.1016/j.intell.2012.01.005
  68. Jo, I., & Bednarz, S. W. (2014). Developing pre-service teachers' pedagogical content knowledge for teaching spatial thinking through geography. Journal of Geography in Higher Education, 38(2), 301–313. https://doi.org/10.1080/03098265.2014.911828
  69. Just, M. A., & Carpenter, P. A. (1985). Cognitive coordinate systems: Accounts of mental rotation and individual differences in spatial ability. Psychological Review, 92(2), 137–172. https://doi.org/10.1037/0033-295X.92.2.137
  70. Kalyankar, V. K. (2019). The van Hiele analysis of curricular materials: A comparative study [Doctoral dissertation, University of Arkansas]. https://scholarworks.uark.edu/etd/3511
  71. Kamii, C., Miyakawa, Y., & Kato, Y. (2004). The development of logico-mathematical knowledge in a block-building activity at ages 1–4. Journal of Research in Childhood Education, 19(1), 13–26. https://doi.org/10.1080/02568540409595053
  72. *Kastens, K. A., & Ishikawa, T. (2006). Spatial thinking in the geosciences and cognitive sciences: A cross-disciplinary look at the intersection of the two fields. In C. A. Manduca & D. W. Mogk (Eds.), Earth and mind: How geologists think and learn about the Earth (pp. 53–76). Geological Society of America. https://doi.org/10.1130/2006.2413(05)
  73. *Kersh, J., Casey, B., & Young, J. M. (2008). Research on spatial skills and block building in girls and boys: The relationship to later mathematics learning. In B. Spodek & O. N. Saracho (Eds.), Mathematics, science, and technology in early childhood education (pp. 233–251). Information Age Publishing.
  74. Kirkwood, M. W., Weiler, M. D, Bernsetin, J. H., Forbes, P. W., & Waber, D. P. (2001). Sources of poor performance on the Rey-Osterrieth Complex Figure Test among children with learning difficulties: A dynamic assessment approach. The Clinical Neuropsychologist, 15(3), 345–356. https://doi.org/10.1076/clin.15.3.345.10268
  75. Kosslyn, S. M. (1983). Ghosts in the mind’s machine. W. W. Norton.
  76. Kozhevnikov, M., Hegarty, M., & Mayer, R. E. (2002). Revising the visualizer–verbalizer dimension: Evidence for two types of visualizers. Cognition and Instruction, 20(1), 47–77. https://doi.org/10.1207/S1532690XCI2001_3
  77. Kozhevnikov, M., Kosslyn, S., & Shephard, J. (2005). Spatial versus object visualizers: A new characterization of visual cognitive style. Memory & Cognition, 33(4), 710–726. https://doi.org/10.3758/BF03195337
  78. Krippendorff, K. (2019). Content analysis: An introduction to its methodology (4th ed.). SAGE. https://doi.org/10.4135/9781071878781
  79. Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. University of Chicago Press.
  80. Landau, B. (1996). Multiple geometric representations of objects in languages and language learners. In P. Bloom, M. A. Peterson, L. Nadel & M. F. Garrett (Eds.), Language and space (pp. 317–363). MIT Press.
  81. LeCompte, M. D. (2000). Analyzing qualitative data. Theory Into Practice, 39(3), 146–154. https://doi.org/10.1207/s15430421tip3903_5
  82. *Lehrer, R., Jenkins, M., & Osana, H. (1998). Longitudinal study of children’s reasoning about space and geometry. In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 137–167). Lawrence Erlbaum Associates.
  83. Leighton, J. P., & Gierl, M. J. (2007). Defining and evaluating models of cognition used in educational measurement to make inferences about examinee’s thinking processes. Educational Measurement: Issues and Practice, 26(2), 3–16. https://doi.org/10.1111/j.1745-3992.2007.00090.x
  84. †Levine, S. C., Huttenlocher, J., Taylor, A., & Langrock, A. (1999). Early sex differences in spatial skill. Developmental Psychology, 35(4), 940–949. https://doi.org/10.1037//0012-1649.35.4.940.
  85. †Liben, L. S. (1988). Conceptual issues in the development of spatial cognition. In J. Stiles-Davis, M. Kritchevsky, & U. Bellugi (Eds.), Spatial cognition: Brain bases and development (pp. 145–201). Lawrence Erlbaum Associates.
  86. *Liben, L. S., & Downs, R. M. (1989). Understanding maps as symbols: The development of map concepts in children. Advances in Child Development and Behavior, 22, 145–201. https://doi.org/10.1016/S0065-2407(08)60414-0
  87. *Liben, L. S., & Yekel, C. A. (1996). Preschoolers’ understanding of plan and oblique maps: The role of geometric and representational correspondence. Child Development, 67(6), 2780–2796. https://doi.org/10.2307/1131752
  88. Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. Sage.
  89. Lohman, D. F. (1979). Spatial ability: Review and re-analysis of the correlational literature (Technical Report No. 8). Stanford University, School of Education, Aptitude Research Project.
  90. Lord, T. R., & Rupert, J. L. (1995). Visual-spatial aptitude in elementary education majors in science and math tracks. Journal of Elementary Science Education, 7(2), 47–58. https://doi.org/10.1007/BF03173735
  91. *Loewenstein, J., & Gentner, D. (2001). Spatial mapping in preschoolers: Close comparisons facilitate far mappings. Journal of Cognition and Development, 2(2), 189–219. https://doi.org/10.1207/S15327647JCD0202_4
  92. Lowrie, T., Logan, T., & Patahuddin, S. M. (2018). A learning design for developing mathematics understanding: The ELPSA framework. The Australian Mathematics Teacher, 74(4), 26-31. https://doi.org/10.3316/informit.209943391982726
  93. Mackay, C. K., Brazendale, A. H., & Wilson, L. F. (1972). Concepts of horizontal and vertical: A methodological note. Developmental Psychology, 7(3), 232–237. https://doi.org/10.1037/h0033344
  94. Mamolo, A., Sinclair, M., & Whiteley, W. (2011). Filling the pyramid: An activity in proportional reasoning. Mathematics Teaching in the Middle School, 16(9), 545–551. https://doi.org/ 10.5951/MTMS.16.9.0544
  95. McGee, M. G. (1979). Human spatial abilities: Sources of sex differences. Praeger.
  96. Merleau-Ponty, M. (1962). Phenomenology of perception. (C. Smith, Trans.) Routledge Classics. (Original work published 1945).
  97. Merriam, S. B. (1998). Qualitative research and case study applications in education: Revised and expanded from case study research in education. Jossey-Bass.
  98. Merriam-Webster. (n.d.). Merriam-Wester.com dictionary. Retrieved January 10, 2023, from https://www.merriam-webster.com/
  99. Miles, M. B., Huberman, A. M., & Saldaña, J. (2014). Qualitative data analysis: A methods sourcebook (3rd ed.). Sage.
  100. *Mix, K. S., & Cheng, Y. L. (2012). The relation between space and math: Developmental and educational implications. Advances in Child Development and Behavior, 42, 197–243. https://doi.org/10.1016/B978-0-12-394388-0.00006-X
  101. Mohan, A., & Mohan, L. (2014). Spatial thinking through the elementary years. Social Studies Review, 53, 52–59.
  102. *Möhring, W., Newcombe, N. S., & Frick, A. (2014). Zooming in on spatial scaling: Preschool children and adults use mental transformations to scale spaces. Developmental Psychology, 50(5), 1614–1619. https://doi.org/10.1037/a0035905
  103. Moss, J., Bruce, C. D., Caswell, B., Flynn, T., & Hawes, Z. (2016). Taking shape: Activities to develop geometric and spatial thinking, Grades K-2. Pearson.
  104. Moss, J., Hawes, Z., Naqvi, S., & Caswell, B. (2015). Adapting Japanese lesson study to enhance the teaching and learning of geometry and spatial reasoning in early years classrooms: A case study. ZDM: The International Journal on Mathematics Education, 47(3), 377–390. https://doi.org/10.1007/s11858-015-0679-2
  105. *Moyer, J. C. (1978). The relationship between the mathematical structure of Euclidean transformations and the spontaneously developed cognitive structures of young children. Journal for Research in Mathematics Education, 9(2), 83–92. https://doi.org/10.2307/748871
  106. *Muir, S. P., & Cheek, H. N. (1986). Mathematics and the map skill curriculum. School Science and Mathematics, 86(4), 284–291. https://doi.org/10.1111/j.1949-8594.1986.tb11620.x
  107. Mulligan, J. (2015). Looking within and beyond the geometry curriculum: Connecting spatial reasoning to mathematics learning. ZDM, 47(3), 511–517. https://doi.org/10.1007/s11858-015-0696-1
  108. Mulligan, J. T., & Mitchelmore, M. C. (2009). Awareness of pattern and structure in early mathematical development. Mathematics Education Research Journal, 21(2), 33-49. https://doi.org/10.1007/BF03217544
  109. Myers, L. J., & Liben, L. S. (2008). The role of intentionality and iconicity in children’s developing comprehension and production of cartographic symbols. Child Development, 79(3), 668–684. https://doi.org/10.1111/j.1467-8624.2008.01150.x
  110. National Association for the Education of Young Children & National Council of Teachers of Mathematics. (2010). Early childhood mathematics: Promoting good beginnings: A joint position statement of the National Association for the Education of Young Children (NAEYC) and the National Council of Teachers of Mathematics (NCTM), adopted in 2002, updated in 2010. National Association for the Education of Young Children. https://www.naeyc.org/sites/default/files/globally-shared/downloads/PDFs/resources/position-statements/psmath.pdf
  111. National Commission on Excellence in Education. (1983). A nation at risk: The imperative for educational reform. Government Printing Office.
  112. *National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. https://www.nctm.org/Standards-and-Positions/Principles-and-Standards/
  113. National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Authors.
  114. *National Research Council. (2006). Learning to think spatially. National Academies Press. https://doi.org/10.17226/11019
  115. Newcombe, N. S. (1989). The development of spatial perspective taking. In H. W. Reese (Ed.), Advances in child development and behavior (Vol. 22, pp. 203–247). New York: Academic Press.
  116. Newcombe, N. S. (2013). Seeing relationships: Using spatial thinking to teach science, mathematics, and social studies. American Educator, 37(1), 26–31. https://files.eric.ed.gov/fulltext/EJ1006210.pdf
  117. Newcombe, N. (2017). Harnessing spatial thinking to support STEM learning [Working Paper No. 161]. Organisation for Economic Co-operation and Development. https://doi.org/10.1787/7d5dcae6-en
  118. *Newcombe, N. S., & Huttenlocher, J. (2000). Making space: The development of spatial representation and reasoning. MIT Press
  119. *Newcombe, N. S., & Shipley, T. F. (2014). Thinking about spatial thinking: New typology, new assessments. In J. S. Gero (Ed.), Studying visual and spatial reasoning for design creativity (pp. 179–192). Springer. https://doi.org/10.1007/978-94-017-9297-4_10
  120. *Newcombe, N. S., & Sluzenski, J. (2004). Starting points and change in early spatial development. In G. L. Allen (Ed.), Human spatial memory: Remembering where (pp. 25–40). Lawrence Erlbaum Associates.
  121. Northwestern University. (2023). Welcome to SILC: Resources. https://www.silc.northwestern.edu/resources_2/
  122. Oxford University Press. (2022). Oxford English dictionary. https://www.oed.com/
  123. Parks, A. N., & Wager, A. A. (2015). What knowledge is shaping teacher preparation in early childhood mathematics? Journal of Early Childhood Teacher Education, 36(2), 124–141. https://doi.org/10.1080/10901027.2015.103052
  124. *Perham, F. (1978). An investigation into the effect of instruction on the acquisition of transformation geometry concepts in first grade children and subsequent transfer to general spatial ability. In R. Lesh & D. Mierkiewicz (Eds.), Concerning the development of spatial and geometric concepts (pp. 229–241). ERIC Clearinghouse for Science, Mathematics, and Environmental Education.
  125. Perry, L., Pinilla, R., Geller, J., Hatfield, C., & Ketterlin-Geller, L. (2020). Spatial reasoning: Learning progressions development (Technical Report No. 20-06). Southern Methodist University, Research in Mathematics Education.
  126. Pinilla, R. K. (2023). Understanding how early childhood educators teach spatial reasoning through mathematics [Doctoral dissertation, Southern Methodist University]. Teaching and Learning Theses and Dissertations. https://scholar.smu.edu/simmons_dtl_etds/15/
  127. Porter, A., McMaken, J., Hwang, J., & Yang, R. (2011). Common Core Standards: The new U.S. intended curriculum. Educational Researcher, 40(3), 103–116. https://doi.org/10.3102/0013189X11405038
  128. *Presmeg, N. C. (1997). Generalization using imagery in mathematics. In L. D. English (Ed.), Mathematical reasoning: Analogies, metaphors, and images (pp. 299–312). Lawrence Erlbaum Associates.
  129. Radford, L. (2014). Towards an embodied, cultural, and material conception of mathematics cognition. ZDM: The International Journal on Mathematics Education, 46, 349–361. https://doi.org/10.1007/s11858-014-0591-1
  130. Rieser, J. J., Doxsey, P. A., McCarrell, N. S., & Brooks, P. H. (1982). Wayfinding and toddlers’ use of information from an aerial view. Developmental Psychology, 18(5), 714–720. https://doi.org/10.1037/0012-1649.18.5.714
  131. *Rieser, J. J., Garing, A. E., & Young, M. F. (1994). Imagery, action, and young children’s spatial orientation: It’s not being there that counts, it’s what one has in mind. Child Development, 65(5), 1262–1278. https://doi.org/10.2307/1131498
  132. Roberts, R. J., Jr., & Aman, C. J. (1993). Developmental differences in giving directions: Spatial frames of reference and mental rotation. Child Development, 64(4), 1258–1270. https://doi.org/10.2307/1131338
  133. Rosser, R. A. (1994). The developmental course of spatial cognition: Evidence for domain multidimensionality. Child Study Journal, 24(4), 255–280.
  134. Rosser, R. A., Lane, S., & Mazzeo, J. (1988). Order of acquisition of related geometric competencies in young children. Child Study Journal, 18(2), 75–90.
  135. Rush, G. M., & Moore, D. M. (1991). Effects of restructuring training and cognitive style. Educational Psychology, 11(3– 4), 309 –321. https://doi.org/10.1080/0144341910110307
  136. Saldaña, J. (2016). The coding manual for qualitative researchers (3rd ed.). Sage.
  137. *Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. Routledge.
  138. *Sarama, J., Clements, D. H., Swaminathan, S., McMillen, S., & González Gómez, R. M. (2003). Development of mathematical concepts of two-dimensional space in grid environments: An exploratory study. Cognition and Instruction, 21(3), 285–324. https://doi.org/10.1207/S1532690XCI2103_03
  139. *Sarama, J., Clements, D. H., & Vukelic, E. B. (1996). The role of a computer manipulative in fostering specific psychological/mathematical processes. In E. Jakubowski, D. Watkins, & H. Biske (Eds.), Proceedings of the 18th annual meeting of the North America Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 567–572). ERIC Clearinghouse for Science, Mathematics, and Environmental Education.
  140. Scholnick, E. K., Fein, G. G., & Campbell, P. F. (1990). Changing predictors of map use in wayfinding. Developmental Psychology, 26(2), 188–193. https://doi.org/10.1037/0012-1649.26.2.188
  141. Schultz, K. A., & Austin, J. D. (1983). Directional effects in transformational tasks. Journal for Research in Mathematics Education, 14(2), 95–101. https://doi.org/10.2307/748577
  142. Seo, K.-H., & Ginsburg, H. P. (2004). What is developmentally appropriate in early childhood mathematics education? Lessons from new research. In D. H. Clements, J. Sarama, & A.-M. DiBiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 91–104). Erlbaum. https://doi.org/10.4324/9781410609236
  143. Serbin, L. A., & Connor, J. M. (1979). Sex-typing of children’s play preferences and patterns of cognitive performance. The Journal of Genetic Psychology, 134(2), 315–316. https://doi.org/10.1080/00221325.1979.10534065
  144. Shepard, R. N., & Metzler, J. (1971). Mental rotation of three-dimensional objects. Science, 171(3972), 701–703. https://doi.org/10.1126/science.171.3972.701
  145. Shepard, R. N., & Cooper, L. A. (1982). Mental images and their transformations. MIT Press.
  146. Siegel, A. W., & White, S. H. (1975). The development of spatial representations of large-scale environments. In H. W. Resse (Ed.), Advances in child development and behavior (Vol. 10, pp. 9–55). Academic Press.
  147. Simon, H. A. (2001). Observations on the sciences of science learning. Journal of Applied Developmental Psychology 21(1), 115–121. https://doi.org/10.1016/S0193-3973(99)00055-6
  148. Sinclair, N., & Bruce, C.D. (2015). New opportunities in geometry education at the primary school. ZDM Mathematics Education, 47, 319–329. https://doi.org/10.1007/s11858-015-0693-4
  149. Sorby, S.A., & Panther, G.C. (2020). Is the key to better PISA math scores improving spatial skills? Mathematics Education Research Journal, 32, 213–233. https://doi.org/10.1007/s13394-020-00328-9
  150. *Steenpaß, A., & Steinbring, H. (2013). Young students’ subjective interpretations of mathematical diagrams: Elements of the theoretical construct “frame-based interpreting competence.” ZDM: The International Journal on Mathematics Education, 46, 3–14. https://doi.org/10.1007/s11858-013-0544-0
  151. *Stieff, M. (2007). Mental rotation and diagrammatic reasoning in science. Learning and Instruction, 17(2), 219–234. https://doi.org/10.1016/j.learninstruc.2007.01.012
  152. Steffe, L. P., & Cobb, P. (1988). Construction of arithmetical meanings and strategies. Springer-Verlag.
  153. Stiles, J. (2001). Spatial cognitive development. In C. A. Nelson & M. Luciana (Eds.), Handbook of developmental cognitive neuroscience (pp. 399–414). Bradford.
  154. *Suwa, M., & Tversky, B. (1997). What do architects and students perceive in their design sketches? A protocol analysis. Design Studies 18(4), 385–403. https://doi.org/10.1016/S0142-694X(97)00008-2
  155. Tahta, D. (1980). About geometry. For the Learning of Mathematics, 1(1), 2–9.
  156. *Taylor, H. A., & Hutton, A. (2013). Think3d!: training spatial thinking fundamental to STEM Education. Cognition and Instruction, 31(4), 434–455. https://doi.org/10.1080/07370008.2013.828727
  157. Thom, J., & McGarvey, L. (2015). The act and artifact of drawing(s) in mathematics: Observing geometric thinking through children’s drawings. ZDM: The International Journal on Mathematics Education, 47(3), 465–481. https://doi.org/10.1007/s11858-015-0697-0
  158. Thurston, W. (1995). On proof and progress in mathematics. For the Learning of Mathematics, 15(1), 29–37.
  159. Tzuriel, D., & Egozi, G. (2010). Gender differences in spatial ability of young children: The effects of training and processing strategies. Child Development, 81(5), 1417–1430. https://doi.org/ 10.1111/j.1467-8624.2010.01482.x
  160. *Uttal, D. H. (1996). Angles and distances: Children’s and adults’ reconstruction and scaling of spatial configurations. Child Development, 67(6), 2763–2779. https://doi.org/10.2307/1131751
  161. *Uttal, D. H., Meadow, N. G., Tipton, E., Hand, L. L., Alden, A. R., Warren, C., & Newcombe, N. S. (2013). The malleability of spatial skills: A meta-analysis of training studies. Psychological Bulletin, 139(2), 352–402. https://doi.org/10.1037/a0028446
  162. *Vasilyeva, M., & Bowers, E. (2006). Children’s use of geometric information in mapping tasks. Journal of Experimental Child Psychology, 95(4), 255–277. https://doi.org/10.1016/j.jecp.2006.05.001
  163. *Vasilyeva, M., & Huttenlocher, J. (2004). Early development of scaling ability. Developmental Psychology, 40(5), 682–690. https://doi.org/10.1037/0012-1649.40.5.682
  164. *Voyer, D., Postma, A., Brake, B., & Imperato-McGinley, J. (2007). Gender differences in object location memory: A meta-analysis. Psychonomic Bulletin & Review, 14(1), 23–38. https://doi.org/10.3758/BF03194024
  165. *Vurpillot, E. (1976). The visual world of the child. International Universities Press.
  166. Wai, J., Lubinski, D., & Benbow, C. P. (2009). Spatial ability for STEM domains: Aligning over 50 years of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology, 101(4), 817–835. https://doi.org/10/1037/a0016127
  167. Wang, R. F., & Spelke, E. S. (2002). Human spatial representation: Insights from animals. Trends in Cognitive Sciences, 6(9), 376–382. https://doi.org/10.1016/S1364-6613(02)01961-7
  168. Wheatley, G. (1996). Quick draw: Developing spatial sense in mathematics. Florida Department of Education.
  169. Wheatley, G. H. (1990). One point of view: Spatial sense and mathematics learning. Arithmetic Teacher, 37(6), 10–11. https://doi.org/10.5951/AT.37.6.0010
  170. *Williford, H. J. (1972). A study of transformational geometry instruction in the primary grades. Journal for Research in Mathematics Education, 3(4), 260–271. https://doi.org/10.2307/748493
  171. Wright, R., Thompson, W., Ganis, G., Newcombe, N., & Kosslyn, S. (2008). Training generalized spatial skills. Psychonomic Bulletin and Review, 15(4), 763–771. https://doi.org/10.3758/PBR.15.4.763
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