Spatial reasoning in the early years: Principles, assertions, and speculations

Spatial Reasoning in the Early Years: Principles, Assertions, and Speculations

Volumn , Issue , 2015, Pages 1-176

  Davis, Brent ^a  

^a UNIVERSITY OF CALGARY   (Canada)

Author keywords

[No Author keywords available]

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EID: 85120541844     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.4324/9781315762371     Document Type: Book

References (304)

1. Alibali, M. W., & Nathan, M. J. (2007). Teachers' gestures as a means of scaffolding students' understanding: evidence from an early algebra lesson. In R. Goldman, R. Pea, B. Barron, & S. J. Derry (Eds.), Video research in the learning sciences. Mahwah, NJ: Erlbaum.
2. American Psychiatric Association. (2013). Diagnostic and statistical manual of mental disorder (5th ed.). Washington, DC: American Psychiatric Publishing.
3. th century. London Mathematics Society, 34, 1-15.
4. Baartmans, B. G., & Sorby, S. A. (1996). Making connections: spatial skills and engineering drawings. The Mathematics Teacher, 89, 348-357.
5. Baddeley, A. D. (1986). Working memory. Oxford, UK: Oxford University Press.
6. Baddeley, A. D., & Hitch, G. (1974). Working memory. In G. H. Bower (Ed.), The psychology of learning and motivation: advances in research and theory (Vol. 8, pp. 47-89). New York: Academic Press.
7. Baddeley, A. D., & Logie, R. H. (1999). Working memory: the multiple component model. In A. Miyake & P. Shah (Eds.), Models of working memory: mechanisms of active maintenance and executive control (pp. 28-61). New York: Cambridge University Press.
8. Bagust, J., Docherty, S., Haynes, W., Telford, R., & Isableu, B. (2013). Changes in Rod and Frame Test scores recorded in schoolchildren during development - a longitudinal study. PLoS ONE, 8(5): e65321. doi: 10.1371/journal. pone.0065321
9. Balacheff, N. (1988). Aspects of proof in pupils' practice of school mathematics (D. Pimm, Trans.). In D. Pimm (Ed.), Mathematics, teachers and children (pp. 216-235). London: Hodder & Stoughton
10. Baldy, R., Devichi, C., & Chatillon, J.-F. (2004). Developmental effects in 2D versus 3D versions in verticality and horizontality tasks. Swiss Journal of Psychology, 63(2), 75-83.
11. Barr, R. (2010). Transfer of learning between 2D and 3D sources during infancy: informing theory and practice. Developmental Review, 30(2), 128-154. doi: 10.1016/j.dr.2010.03.001
12. Bateson, G. (1972). Steps to an ecology of mind: collected essays in anthropology, psychiatry, evolution, and epistemology. Chicago: University of Chicago Press.
13. Benbow, C. P. (2012). Identifying and nurturing future innovators in science, technology, engineering, and mathematics: a review of findings from the study of mathematically precocious youth. Peabody Journal of Education, 87(1), 16-25. doi:10.1080/0161956X.2012.642236
14. Bénézet, L. P. (1935a, 1935b, 1936). The teaching of arithmetic I, II, III: the story of an experiment. Journal of the National Education Association, 24(8), 241-244; 24(9), 301-303; 25(1), 7-8.
15. Berger, S. E. (2010). Locomotor expertise predicts infants' perseverative errors. Developmental Psychology, 46(2), 326-336.
16. Bernstein, R. J. (1983). Beyond objectivism and relativism: science, hermeneutics, and praxis. Philadelphia, PA: University of Pennsylvania Press.
17. Bishop, A. J. (1980). Spatial abilities and mathematics education: a review. Educational Studies in Mathematics, 11, 257-269.
18. Bishop, A. J. (1983). Space and geometry. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes. New York: Academic Press.
19. Bishop, A. J. (1986). What are some obstacles to learning geometry? Studies in mathematics education, UNESCO, 5, 141-159.
20. th Annual Meeting of the International Group for the Psychology of Mathematics Education, 1, 170-176.
21. Bishop, A. J. (1988b). Mathematics education in its cultural context. Educational Studies in Mathematics, 19(2), 179-191.
22. Bishop, A. J. (2008). Visualising and mathematics in a pre-technological culture. In P. Clarkson & N. Presmeg (Eds.), Critical issues in mathematics education (pp. 109-119). New York, NY: Springer. Retrieved from http://link.springer.com.ezproxy.lib.ucalgary.ca/chapter/10.1007/978-0-387-09673-5_8.
23. Bishop, A. J., Clements, K., Keitel, C., Kilpatrick, J., & Laborde, C. (1996). International handbook of mathematics education. New York: Springer.
24. Black, J., Segal, A., Vitale, J., & Fadjo, C. (2012). Embodied cognition and learning environment design. In D. Jonassen & S. Land (Eds.), Theoretical foundations of learning environments, 2nd ed. (pp. 198-223). New York: Routledge.
25. Black, J., Turner, T. J., & Bower, G. H. (1979). Point of view in narrative comprehension, memory and production. Journal of Verbal Learning and Verbal Behavior, 18, 187-198.
26. Bomba, P. C. (1984). The development of orientation categories between 2 and 4 months of age. Journal of Experimental Child Psychology, 37, 607-636.
27. Booth, J. L., & Siegler, R. S. (2008). Numerical magnitude representations influence arithmetic learning. Child Development, 79(4), 1016-1031.
28. Boswell, S. L. (1976). Young children's processing of asymmetrical and symmetrical patterns. Journal of Experimental Child Psychology, 22(2), 309-318.
29. Bowers, C. A. (2011). Perspectives on the ideas of Gregory Bateson, ecological intelligence, and educational reforms. Eugene, OR: Eco-Justice Press LLC.
30. Brosterman, N. (1997). Inventing Kindergarten. Self published.
31. Bruce, C., Flynn, T., & Moss, J. (2013). A "no-ceiling" approach to young children's mathematics: preliminary results of an innovative professional learning program. In M. Martinez & A. Castro Superfine (Eds.), Proceedings of the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Chicago, IL: University of Chicago.
32. Bruce, C. D., & Hawes, Z. (in press). The role of 2D and 3D mental rotation in mathematics for young children: What is it? Why is it important? And what can we do about it? ZDM: The International Journal on Mathematics Education. 10/2014; doi: 10.1007/s11858-01406374?sa_campaign=email/event/articleAuthor/ onlineFirst
33. Bruce, C. D., Moss, J., Sinclair, N., Whiteley, W., Okamoto, Y., McGarvey, L., Drefs, M., Francis-Pocente, K., & Davis, B. (2013). Early-years spatial reasoning: learning, teaching, and research implications. Research symposium presented at Research Presession Conference of the Annual Meeting of the National Council of Teachers of Mathematics. Denver, CO.
34. Bruner, J. (1966) Toward a theory of instruction. Cambridge, MA: Harvard University Press.
35. Bryant, P. E. (2008). Paper 5: Understanding spaces and its representation in mathematics. In T. Nunez, P. Bryant, & A. Watson (Eds.), Key understandings in mathematics learning: a report to the Nuffield Foundation. Retrieved 28.04.2013 from http://www.nuffieldfoundation.org/sites/default/files/P5.pdf
36. Bryant, P. E. (1973). Discrimination of mirror images by young children. Journal of Comparative Physiological Psychology, 82, 415-425.
37. Bryant, P. E. (1969). Perception and memory of the orientation of visually presented lines by children. Nature, 224, 1331-1332.
38. Burton, L. (2004). Mathematicians as enquirers: learning about learning mathematics. Dordrecht: NL: Springer.
39. Busch, J. C., Watson, J. A., Brinkley, V., Howard, J. R., & Nelson, C. (1993). Preschool embedded figures test performance of young children: age and gender differences. Perceptual and Motor Skills, 77(2), 491-496.
40. Cakmak, S., Isiksal, M., & Koc, Y. (2014). Investigating effect of origami-based instruction on elementary students' spatial skills and perceptions. The Journal of Educational Research, 107(1), 59-68.
41. Campbell, S. R. (2010). Embodied minds and dancing brains: new opportunities for research in mathematics education. In B. Sriaman & L. English (Eds.), Theories of mathematics education (pp. 309-331). Berlin: Springer Berlin.
42. Campbell, S. R. (2011). Educational neuroscience: motivations, methodology, and implications. In K. E. Patten & S. R. Campbell (Eds.), Educational neuroscience: initiatives and emerging issues (pp. 7-16). Hoboken, NJ: Wiley-Blackwell.
43. Carter, N. (2009). Visual group theory. New York: Mathematical Association of America.
44. 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. Serial 246.
45. 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.
46. 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, 29-48.
47. Caswell, B., Moss, J., Hawes, Z., & Naqvi, S. (2013). Math for young children (M4YC) project: a no-ceiling approach to math learning in an urban school. Centre for Urban Schooling, 1(1), 1-4.
48. Châtelet, G. (2000/1993). Les enjeux du mobile. Paris: Seuil. (Engl. transl., by R. Shore & M. Zagha: Figuring space: Philosophy, Mathematics and Physics). Dordrecht: Kluwer Academy Press.
49. 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, 1-22.
50. Cheng, Y.-L., & Mix, K. S. (2014). Spatial training improves children's mathematics ability. Journal of Cognition and Development, 15(1), 2-11. doi: 10.1080/15248372.2012.725186
51. Chu, M., & Kita, S. (2011). The nature of gestures' beneficial role in spatial problem solving. Journal of Experimental Psychology: General, 140(1), 102-116.
52. Claessens, A., Duncan, G., & Engel, M. (2009). Kindergarten skills and fifth-grade achievement: evidence from the ECLS-K. Economics of Education Review, 28, 415-427.
53. Claessens, A., & Engel, M. (2011). How important is where you start? Early mathematical knowledge and later school success. Paper presented at the 2011 Annual Meeting of the American Educational Research Association (AERA), New Orleans, LA. April 2011.
54. Clearfield, M. W. (2004). The role of crawling and walking experience in infant spatial memory. Journal of Experimental Child Psychology, 89(3), 214-241.
55. Clements, D. H. (2004). Geometric and spatial thinking in early childhood education. In D. H. Clements, J. Sarama, & A.-M. Di Biase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 267-298). Mahwah, NJ: Lawrence Earlbaum Associates, Inc.
56. Clements, D. H., & Sarama, J. (2004). Mathematics everywhere, every time. Teaching Children Mathematics, 10(8), 421-426.
57. Clements, D. H., & Sarama, J. (2011). Early childhood teacher education: the case of geometry. Journal of Mathematics Teacher Education, 14(2), 133-148.
58. 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.
59. Clements, D. H., Wilson, D. C., & Sarama, J. (2004). Young children's composition of geometric figures: A learning trajectory. Mathematical Thinking and Learning, 6(2), 163-184.
60. Clements, M. A. (1982). Visual imagery and school mathematics. For the Learning of Mathematics, 2, 2-9, & 3, 33-39.
61. Clements, M. A. (2008). Spatial abilities, mathematics, culture, and the Papua New Guinea experience. In P. Clarkson & N. Presmeg (Eds.), Critical issues in mathematics education (pp. 97-106). New York, NY: Springer. Retrieved from http://link.springer.com.ezproxy.lib.ucalgary.ca/chapter/10.1007/978-0-387-09673-5_7
62. Coates, S. W. (1972). Preschool embedded figures test. Palo Alto, CA: Consulting Psychologists Press.
63. Cohn, N. (2014). Framing "I can't draw": The influence of cultural frames on the development of drawing. Culture and Psychology, 20(1), 102-117.
64. Cook, S. W., Mitchell, Z. & Goldin-Meadow, S. (2008). Gesturing makes learning last. Cognition, 106(2), 1047-1058.
65. Coxeter, H. S. M. et al. (1967). Geometry Curriculum K-13. Toronto: OISE/UofT 1967. http://wiki.math.yorku.ca/index.php/CMEF_Geometry_Curriculum
66. Cutting, J. E. (2002). Representing motion in a static image: constraints and parallels in art, science, and popular culture. Perception, 31, 1165-1193.
67. D'Ambrosio, U. (1985). Ethnomathematics and its place in the history and pedagogy of mathematics. For the Learning of Mathematics, 5(1), 44-48.
68. Davis, B. (1996). Teaching mathematics: toward a sound alternative. New York: Garland.
69. Davis, B. (2011). Mathematics teachers' subtle, complex disciplinary knowledge. Science, 332, 1506-1507.
70. nd ed.). New York: Routledge.
71. de Freitas, E., & Sinclair, N. (2012). Diagram, gesture, agency: theorizing embodiment in the mathematics classroom. Educational Studies in Mathematics, 80(1-2), 133-152.
72. de Freitas, E., & Sinclair, N. (2013). New materialist ontologies in mathematics education: the body in/of mathematics. Educational Studies in Mathematics, 83(3), 453-470.
73. de Hevia, M. D., Vallar, G., & Girelli, L. (2008). Visualizing numbers in the mind's eye: the role of visuo-spatial process in numerical abilities. Neuroscience and Biobehavioral Reviews, 32(8), 1361-1372.
74. Dehaene, S. (2011). The number sense: how the mind creates mathematics, revised edition. Oxford, UK: Oxford University Press.
75. Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122(3), 371-396.
76. DeLoache, J. S. (1987). Rapid change in the symbolic functioning of very young children. Science, 238(4833), 1556-1557.
77. Diamond, J. (2012). The world until yesterday: what can we learn from traditional societies? New York: Penguin Books.
78. Diefes-Dux, H. A., Whittenberg, L., & McKee, R. (2013). Mathematical modeling at the intersection of elementary mathematics, art, and engineering education. In L. D. English & J. T. Mulligan (Eds.), Reconceptualizing early mathematics learning (pp. 309-325). Dordrecht, NL: Springer.
79. Dieudonné, J. (1981). The universal domination of geometry. The Two-Year College Mathematics Journal, 12(4), 227-231.
80. Donaldson, M. (1986). Children's explanations: a psycholinguistic study. Cambridge, UK: Cambridge University Press
81. Doyle, R. A., Voyer, D., & Cherney, I. D. (2012). The relation between childhood spatial activities and spatial abilities in adulthood. Journal of Applied Developmental Psychology, 33(2), 112-120.
82. Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A.C., Klebanov, P., & Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43, 1428-1446.
83. Dreyfus, T. (1994). The role of cognitive tools in mathematics education. In R. Biehler, R. Scholz, R. Strasser, & B. Winkelmann (Eds.), Didactics of mathematics as a scientific discipline (pp. 201-212). Dordrecht: Kluwer.
84. Edwards, L., Nathan, M., Nemirovsky, R., & Soto-Johnson, H. (2013). Embodied cognition: what it means to know and do mathematics. Symposium conducted at the Annual Meeting of the National Council of Teachers of Mathematics (NCTM) Research Pre-session, Denver, CO.
85. Eglash, R. (1999). African fractals: modern computing and indigenous design. New Brunswick, NJ: Rutgers University Press.
86. Ekstrom, R. B., French, J. W., Harman, H. H., & Dermen, D. (1976). Kit of factor-referenced cognitive tests. Princeton, NJ: Educational Testing Service.
87. Ehrlich, S., Levine, S., & Goldin-Meadow, S. (2006). The importance of gesture in children's spatial reasoning. Developmental Psychology, 42(6), 1259-1268.
88. 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.
89. Farmer, G., Verdine, B., Lucca, K., Davies, T., Dempsey, R., Newcombe, N., Hirsh-Pasek, K., & Golmkoff, R. (2013). Putting the pieces together: spatial skills at age 3 predict to spatial and math performance at age 5. Paper presented at the Society for Research in Child Development, Seattle, WA.
90. Fauconnier, G., & Turner, M. (2002). The way we think: conceptual blending and the mind's hidden complexities. New York: Basic Books.
91. Feng, J., Spence, I., & Pratt, J. (2007). Playing an action video game reduces gender differences in spatial cognition. Psychological Science, 18(10), 850-855. doi: 10.1111/j.1467-9280.2007.01990.x
92. Fias, W., Menon, V., & Szucs, D. (2013). Multiple components of developmental dyscalculia. Trends in Neuroscience and Education, 2, 43-47.
93. Fischer, M. H., & Shaki, S. (2014). Spatial associations in numerical cognition: from single digits to arithmetic. Quarterly Journal of Experimental Psychology, 67, 1461-1483. doi: 10.1080/17470218.2014.927515
94. Flavell, J. H. (1999). Cognitive development: children's knowledge about the mind. Annual Review of Psychology, 50(1), 21-45.
95. Fomenko, A. T. (2011). Visual geometry and topology. Berlin: Springer.
96. Fonagy, P., & Target, M. (2007). The rooting of the mind in the body: new links between attachment theory and psychoanalytic thought. Journal of American Psychoanalytic Association, 55(2), 411-456. doi: 10.1111/j.1469-7610.2007.01727.x
97. Frick, A., Daum, M. M., Walser, S., & Mast, F. W. (2009). Motor processes in children's mental rotation. Journal of Cognition and Development, 10, 18-40.
98. Frick, A., Möhring, W., & Newcombe, N. S. (2014). Picturing perspectives: development of perspective-taking abilities in 4- to 8-year-olds. Frontiers in Psychology, 5:386. doi: 10.3389/fpsyg.2014.00386
99. Frick, A., Möhnng, W., & Newcombe, N. S. (in press). Development of mental transformation abilities. Trends in Cognitive Sciences. doi: http://dx.doi.org/10/1016/j.tics.2014.05.011
100. Frick, A., & Newcombe, N. S. (2012). Getting the big picture: development of spatial scaling abilities. Cognitive Development, 27(3), 270-282.
101. Frick, A., & Wang, S. H. (2014). Mental spatial transformations in 14- and 16-month-old infants: effects of action and observational experience. Child Development, 85(1), 278-293. doi: 10.1111/cdev.12116
102. Galton, F. (1880). Visualised numerals. Nature, 21, 252-256.
103. Galton, F. (1881). Visualised numerals. Journal of the Anthropological Institute of Great Britain and Ireland, 10: 85-102.
104. Gattegno, C. (1963). For the teaching of mathematics. Reading, UK: Educational Explores.
105. Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37(4), 4-15.
106. 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.
107. Gerofsky, S. (2014). Making sense of multiple meanings of "embodied mathematics learning." In S. Oesterle, P. Liljedahl, C. Nicol, & D. Allan (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36, vol. 3, pp. 145-152. Vancouver, Canada: PME.
108. Girelli, L., Semenza, C., & Delazer, M. (2004). Inductive reasoning and implicit memory: evidence from intact and impaired memory systems. Neuropsychologia, 42(7), 926-938.
109. Gray, H. (1858). Anatomy of the human body. New York: Lea and Febiger.
110. Gregory, K. M., Kim, A. S., & Whiren, A. (2003). The effect of verbal scaffolding on the complexity of preschool children's block constructions. In D. E. Lytle (Ed.), Play and educational theory and practice: play and culture studies (vol. 5, pp. 117-133). Westport, CT: Praeger.
111. Grissmer, D. W., Mashburn, A. J., Cottone, E., Chen, W. B., Brock, L. L., Murrah, W. M., & Cameron, C. E. (2013). Play-based after-school curriculum improves measures of executive function, visuospatial and math skills and classroom behavior for high risk K-1 children. Paper presented at the Society for Research in Child Development, Seattle, WA.
112. Grumet, M. (1988). Bitter milk: women and teaching. Amherst, MA: University of Massachusetts Press.
113. 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. doi: 10.1037/a0027433
114. Hallowell, D. A., Okamoto, Y., Romo, L. F., & La Joy, J. R. (in press). First-grader's spatial-mathematical reasoning about plane and solid shapes and their representations. ZDM: The International Journal on Mathematics Education.
115. Hanline, M. F., Milton, S., & Phelps, P. (2001). Young children's block construction activities: findings from 3 years of observation. Journal of Early Intervention, 24, 224-237.
116. Happé, F. (2013). Embedded figures test (EFT). In F. R. Volkmar (Ed.), Encyclopedia of autism spectrum disorders [electronic resource] (pp. 1077-1078). New York: Springer.
117. Harris, J., Hirsh-Pasek, K., & Newcombe, N. S. (2013). A new twist on studying the development of dynamic spatial transformations: Mental paper folding in young children. Mind, Brain and Education, 7(1), 49-55.
118. th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Chicago, IL: University of Illinois at Chicago.
119. Hawes, Z., Lefevre, J., Xu, C., & Bruce, C. (in press). Mental rotation with tangible three-dimensional objects: a new measure sensitive to developmental differences in 4- to 8-year-old children. Mind, Brain and Education, 8(4).
120. Hawes, Z., Moss, J., Caswell, B., Naqvi, S., & MacKinnon (in preparation). Enhancing children's spatial and numerical skills through a 'dynamic-spatial' approach to early geometry instruction: effects of a seven-month intervention.
121. Hawkins, D. (2000). The roots of literacy. Boulder, CO: University Press of Colorado.
122. Healy, L., & Fernandes, S. H. A. A. (2011). The role of gestures in the mathematical practices of those who do not see with their eyes. Educational Studies in Mathematics, 77, 157-174.
123. 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. 85-94.
124. Henderson, D. W., & Taimina, D. (2005). Experiencing geometry: Euclidean and non-Euclidean with history, New York: Prentice Hall.
125. Henrich, J., Heine, S. J., & Norenzayan, A. (2010). The weirdest people in the world? Behavioral and Brain Sciences, 33(2-3), 61-83. doi: 10.1017/S0140525X0999152X
126. Hershkowitz, R., Parzysz, B., & Van Dormolen, J. (1996). Space and shape. In A. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International Handbook of Mathematics Education (pp. 61-204). Dordrecht: Kluwer.
127. Hiley, D. R., & Bohman, J. F. (1992). The interpretive turn: philosophy, culture, science. Ithaca, NY: Cornell University Press.
128. Hodgen, J., Pepper, D., Sturman, L., & Ruddick, G. (2010). Is the UK an outlier? An international comparison of upper secondary mathematics education. London: Nuffield Foundation.
129. Hoffman, D. (2000a). Visual intelligence: how we create what we see (new edition). New York: W.W. Norton.
130. Hoffman, D. (2000b). When the world stopped moving. Animated gifs from http://www.cogsci.uci.edu/%7Eddhoff/vi6.html
131. Holmes, J., Gathercole, S. E., & Dunning, D. L. (2009). Adaptive training leads to sustained enhancement of poor working memory in children. Developmental Science, 12(4), 9-15.
132. Howson, A. G. (Ed.). (1973). Developments in mathematical education: Proceedings of the Second International Congress on Mathematical Education. Cambridge, UK: Cambridge University Press.
133. Hubbard, E. M., Piazza, M., Pinel, P., & Dehaene, S. (2009). Numerical and spatial intuitions: a role for posterior parietal cortex? In L. Tommasi, L. Nadel, & M. A. Peterson (Eds.), Cognitive biology: evolutionary and developmental perspectives on mind, brain and behavior (pp. 221-246). Cambridge, MA: MIT Press.
134. Huttenlocher, J., Newcombe, N. S., & Vasilyeva, M. (1999). Spatial scaling in young children. Psychological Science, 10, 393-398.
135. Jardine, D. W. (1994). On the ecologies of mathematical language and the rhythms of the earth. In P. Ernest (Ed.), Mathematics, education, and philosophy: an international perspective (pp. 109-23), London, UK: Falmer.
136. Jaušovec, N., & Jaušovec, K. (2012). Sex differences in mental rotation and cortical activation patterns: Can training change them? Intelligence, 40(2), 151-162.
137. Jmol: an open-source Java viewer for chemical structures in 3D. http://www.jmol.org/
138. Karp, S. A., & Konstadt, N. (1971). Children's Embedded Figures Test. Palo Alto, CA: Consulting Psychologists Press.
139. 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). Boulder, CO: Geological Society of America.
140. Kell, H. J., Lubinski, D., Benbow, C. P., & Steiger, J. H. (2013). Creativity and technical innovation: spatial ability's unique role. Psychological Science, 24(9), 1831-1836. doi: 10.1177/0956797613478615.
141. 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.
142. Kotsopoulos, D., Cordy, M., & Langemeyer, M. (under review). Children's understanding of large-scale mapping tasks: an analysis of talk, drawings, and gesture. ZDM: The International Journal on Mathematics Education.
143. Kotsopoulos, D., Cordy, M., Langemeyer, M., & Khattak, L. (2014). How do children draw, describe, and gesture about motion? In the proceedings of the 11th International Conference of the Learning Sciences (pp. 1-2). Boulder, Colorado.
144. 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.
145. Kozhevnikov, M., Kosslyn, S., & Shephard, J. (2005). Spatial versus object visualizers: a new characterization of visual cognitive style. Memory & Cognition, 33(4), 710-726.
146. Krüger, M., Kaiser, M., Mahler, K., Bartels, W., & Krist, H. (2014). Analogue mental transformations in 3-year-olds: introducing a new mental rotation paradigm suitable for young children. Infant and Child Development, 23(2), 123-138. doi: 10.1002/icd.1815
147. Kyttälä, M., Aunio, P., Lehto, J. E., Van Luit, J., & Hautamaki, J. (2003). Visuospatial working memory and early numeracy. Educational and Child Psychology, 20(3), 65-76.
148. Kyttälä, M., & Lehto, J. (2008). Some factors underlying mathematical performance: the role of visuospatial working memory and non-verbal intelligence. European Journal of Psychology of Education, XXII(1), 77-94.
149. Lakoff, G., & Johnson, M. (1999). Philosophy in the flesh: the embodied mind and its challenge to western thought. New York: Basic Books.
150. Lakoff, G., & Núñez, R. (2000). Where mathematics comes from: how the embodied mind brings mathematics into being. New York: Basic Books.
151. Lee, S. A., Sovrano, V. A., & Spelke, E. S. (2012). Navigation as a source of geometric knowledge: young children's use of length, angle, distance, and direction in a reorientation task. Cognition, 123(1), 144-161.
152. Leikin, R., Berman, A., & Zaslavsky, O. (2000). Applications of symmetry to problem solving. International Journal of Mathematical Education in Science and Technology, 31, 799-809.
153. Levine, S. C., Ratcliff, K. R., Huttenlocher, J., & Cannon, J. (2012). Early puzzle play: a predictor of preschooler's spatial transformation skill. Developmental Psychology, 48, 530-542.
154. Linn, M. C., & Petersen, A. C. (1985). Emergence and characterization of sex differences in spatial ability: a meta-analysis. Child Development, 56, 1479-1498.
155. 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. doi: 10.1023/A:1022116221735
156. Malafouris, L. (2013). How things shape the mind: a theory of material engagement. Cambridge, MA: The MIT Press.
157. Malisza, K. L., Clancy, C., Shiloff, D., Foreman, D., Holden, J., Jones, C., Paulson, K., Summers, R., Yu, C. T., & Chudley, A. E. (2011). Functional evaluation of hidden figures object analysis in children with autistic disorder. Journal of Autism Developmental Disorders, 41, 13-22.
158. Mamolo, A., Sinclair, M., & Whiteley, W. (2011). Filling the pyramid: an activity in proportional reasoning. Mathematics Teaching in the Middle School, 16, 545-551.
159. Mamolo, A., & Whiteley, W. (2012). The Popcorn Box activity and reasoning about optimization. Mathematics Teacher, 105(6), 420-426.
160. Manley, D. B., & Taylor, C. S. (1996). Descartes' meditations. Retrieved from http://www.wright.edu/cola/descartes/synopsis.html
161. Martin, L. C., & Towers, J. (2011). Improvisational understanding in the mathematics classroom. In R. Keith Sawyer (Ed.), Structure and improvisation in creative teaching (pp. 252-278). New York: Cambridge University Press.
162. Martin, L., Towers, J., & Pirie, S. (2006). Collective mathematical understanding as improvisation. Mathematical Thinking and Learning, 8(2), 149-183.
163. Maturana, H. R., & Varela, F. J. (1972). Autopoiesis and cognition: the realization of the living. Dordrecht, NL: Reidel.
164. Maturana, H. R., & Varela, F. J. (1991). The tree of knowledge: the biological roots of human understanding (Rev. ed.). Boston, MA: Random House. (Original work published 1987.)
165. Mazzocco, M. M., & Räsänen, P. (2013). Contributions of longitudinal studies to evolving definitions and knowledge of developmental dyscalculia. Trends in Neuroscience and Education, 2(2), 65-73. doi: 10.1016/j.tine.2013.05.001
166. McAuliffe, C. (2003). Visualizing topography: effects of presentation strategy, gender, and spatial ability (Ph.D. Doctoral dissertation). Arizona State University, Dissertation Abstracts International, Volume: 64-10, Section: A, page: 3653. Retrieved from http://adsabs.harvard.edu/abs/2003PhDT162M(AAI3109579)
167. Menghini, M., Furinghetti, F., Giacardi, L., & Arzarello, F. (Eds.). (2008). The first century of the International Commission on Mathematical Instruction (1908-2008): Reflecting and shaping the world of mathematics education. Rome: Instituto della Enciclopedia Italiana.
168. Merleau-Ponty, M. (1945). Phénoménologie de la perception. Paris: Gallimard.
169. Merleau-Ponty, M. (1962). Phenomenology of perception. (C. Smith, Trans.) New York: Routledge Classics. (Original work published 1945).
170. Merleau-Ponty, M. (1964). Le visible et l'invisible [The visible and invisible]. Paris: Gallimard.
171. Mix, K. S., & Cheng, Y. L. (2012). The relation between space and math: developmental and educational implications. In J. B. Benson (Ed.), Advances in child development and behavior (vol. 42, pp. 197-243). San Diego, CA: Academic Press.
172. Möhnng, 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.
173. Moll, H., Meltzoff, A. N., Merzsch, K., & Tomasello, M. (2013). Taking versus confronting visual perspectives in preschool children. Developmental Psychology, 49(4), 646.
174. Moss, J., Hawes, Z., Chang, D., & Tepylo, D. (2013). From mental rotation task design to lesson planning: the case of the polyomino challenge. Paper presented at Fields MathEd Forum Meeting, Toronto, ON: The Fields Institute for Research in Mathematical Sciences, University of Toronto.
175. Moss, J., Hawes, Z., Naqvi, S., & Caswell, B. (in press). 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).
176. Mulligan, J. T., & Mitchelmore, M. C. (2009). Awareness of pattern and structure in early mathematical development. Mathematics Education Research Journal, 21(2), 33-49.
177. th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Chicago, IL: University of Illinois at Chicago.
178. NASA. (2008). Amino Acid Chirality. Retrieved from http://commons.wikimedia.org/wiki/File:Chirality_with_hands.jpg
179. Nath, S., & Szücs, D. (2014). Construction play and cognitive skills associated with the development of mathematical abilities. Learning and Instruction, 32, 73-80.
180. Nathan, M. J., Eilam, B., & Kim, S. (2007). To disagree, we must also agree: how intersubjectivity structures and perpetuates discourse in a mathematics classroom. The Journal of the Learning Sciences, 16(4), 523-563.
181. National Council of Teachers of Mathematics. (2010). Focus in Grade 1: Teaching with Curriculum Focal Points. Reston, VA: National Council of Teachers of Mathematics.
182. National Research Council. (2006). Learning to think spatially: GIS as a support system in the K-12 curriculum. Washington, DC, The National Academies Press.
183. Needham, T. (2004). Visual complex analysis. New York: Clarendon Press.
184. Nemirovsky, R., Borba, M., Dimattia, C., Arzarello, F., Robutti, O., Schnepp, M., Chazan, D., Ramussen, C., Olszewski, J., Dost, K., Johnson, J. L., Borba, M. C., & Scheffer, N. F. (2004). PME Special Issue: Bodily activity and imagination in mathematics learning. Educational Studies in Mathematics, 57(3), 303-321.
185. Nemirovsky, R., & Ferrara, F. (2009). Mathematical imagination and embodied cognition. Educational Studies in Mathematics, 70(2), 159-174.
186. Nemirovsky, R., Kelton, M. L., & Rhodehamel, B. (2013). Playing mathematical instruments: emerging perceptuomotor integration with an interactive mathematics exhibit. Journal for Research in Mathematics Education, 44(2), 372-415.
187. Newcombe, N. S. (2010). Picture this: increasing math and science learning by improving spatial thinking. American Educator, 34(2), 29-43.
188. Newcombe, N. S. (2014). Thinking about quantity: the intertwined development of spatial and numerical cognition. Paper presented at the Workshop on Making Models, Toronto, ON.
189. Newcombe, N., Huttenlocher, J., Drummey, A. B., & Wiley, J. G. (1998). The development of spatial location coding: place learning and dead reckoning in the second and third years. Cognitive Development, 13(2), 185-200.
190. Newcombe, N. S., & Shipley, T. F. (in press). Thinking about spatial thinking: new typology, new assessments. In J. S. Gero (Ed.), Studying visual and spatial reasoning for design creativity. New York: Springer.
191. Newcombe, N. S., & Stieff, M. (2012). Six myths about spatial thinking. International Journal of Science Education, 34(6), 955-971.
192. Nosworthy, N., Bugden, S., Archibald, L., Evans, B., & Ansari, D. (2013). A two-minute paper-and-pencil test of symbolic and nonsymbolic numerical magnitude processing explains variability in primary school children's arithmetic competence. PLoS ONE 8(7): e67918. doi: 10.1371/journal.pone.0067918
193. Núñez, R. (2003). Do real numbers really move? Language, thought, and gesture: the embodied cognitive foundations of mathematics. In R. Hersh (Ed.), 18 unconventional essays on the nature of mathematics (pp. 160-181). New York: Springer.
194. Núñez, R. E., Edwards, L. D., & Matos, J. F. (1999). Embodied cognition as grounding for situatedness and context in mathematics education. Educational Studies in Mathematics, 39(1-3), 45-65.
195. Okagaki, L., & Frensch, P. A. (1994). Effects of video game playing on measures of spatial performance: gender effects in late adolescence. Journal of Applied Developmental Psychology, 15(1), 33-58.
196. Ong, W. (1982). Orality and literacy: the technologizing of the word. New York: Routledge.
197. Ontario Ministry of Education and Training/OMET. (2005). The Ontario curriculum Grades 1-8 mathematics, Revised. Toronto: Queen's Printer for Ontario.
198. Ormand, C. J., Manduca, C., Shipley, T. F., Tikoff, B., Harwood, C. L., Atit, K., & Boone, A. P. (2014). Evaluating geoscience students' spatial thinking skills in a multi-institutional classroom study. Journal of Geoscience Education, 62(1), 146-154. doi: 10.5408/13-027.1
199. Ormand, C. J., Shipley, T. F., Tikoff, B., Manduca, C. A., Dutrow, B., Goodwin, L., & Resnick, I. (2013, June). Improving spatial reasoning skills in the undergraduate geoscience classroom through interventions based on cognitive science research. Presented at the AAPG Hedberg Conference on 3D Structural Geologic Interpretation, Reno, Nevada. Retrieved from http://spatiallearning.org/media/silc_pdfs/resources/testsandinstruments/tandi-images/crystal_slicing_test.jpg
200. Pascual-Leone, J., & Morra, S. (1991). Horizontality of water level: a neo-piagetian developmental review. In H. W. Reese (Ed.), Advances in Child Development and Behavior (Vol. 23, pp. 231-276). New York: Academic Press.
201. Piaget, J., & B. Inhelder (1967/1948). The child's conception of space. (F. J. Langdon & J. L. Lunzer, Trans.). New York: Norton.
202. Piaget, J., Inhelder, B., & Szeminska, A. (1960). The child's conception of geometry. London: Routledge and Kegan Paul.
203. Pickering, A. (1995). The mangle of practice: time, agency and science. Chicago: University of Chicago Press.
204. Pirie, S., & Kieren, T. (1994). Growth in mathematical understanding: how can we characterise it and how can we represent it? Educational Studies in Mathematics, 26(2-3), 165-190.
205. Pirie, S. E. B., & Thom, J. S. (2001). Thinking through ecological metaphors in mathematics education. In S. Gunn & A. Begg (Eds.), Mind, body, and society: emerging understandings of knowing and learning (pp. 45-52). Melbourne, AU: University of Melbourne.
206. Poirier, L. (2007). Teaching mathematics and the Inuit community. Canadian Journal of Science, Mathematics, & Technology Education, 7(1), 53-67.
207. Presmeg, N. C. (1986). Visualization in high school mathematics. For the Learning of Mathematics, 6(3), 42-46.
208. Presmeg, N. (2008). Spatial abilities research as a foundation for visualization in teaching and learning mathematics. In P. Clarkson & N. Presmeg (Eds.), Critical Issues in Mathematics Education (pp. 83-95). New York: Springer.
209. Pruden, S. M., Levine, S. C., & Huttenlocher, J. (2011). Children's spatial thinking: does talk about the spatial world matter? Developmental Science, 14(6), 1417-1430. doi: 10.1111/j.1467-7687.2011.01088.x
210. Pulvermüller, F. (2011). Meaning and the brain: the neurosemantics of referential, interactive, and combinatorial knowledge. Journal of Neurolinguistics, 25(5), 423-459.
211. Quaiser-Pohl, C., Lehmann, W., & Eid, M. (2004). The relationship between spatial abilities and representations of large-scale space in children - a structural equation modeling analysis. Personality and Individual Differences, 36(1), 95-107.
212. Quinn, P. C., Siqueland, E. R., & Bomba, P. C. (1985). Delayed recognition memory for orientation by human infants. Journal of Experimental Child Psychology, 40(2), 293-303.
213. Radford, L. (2002). The seen, the spoken and the written: a semiotic approach to the problem of objectification of mathematical knowledge. For the Learning of Mathematics, 22(2), 1423.
214. Radford, L. (2014). Towards an embodied, cultural, and material conception of mathematics cognition. ZDM: The International Journal on Mathematics Education, 46, 349-361.
215. th Conference of the International Group for the Psychology of Mathematics Education (pp. 55-62). Honolulu, HI: University of Hawaii.
216. Radford, L., Edwards, L., & Arzarello, F. (2009). Introduction: beyond words. Educational Studies in Mathematics, 70(2), 91-95.
217. Ramey, J., & Uttal, D. H. (2014). Distributed spatial sensemaking in middle school engineering learning, SILC Showcase, November 2014, http://bit.ly/1sNA3OJ
218. Reifel, S., & Greenfield, P. M. (1983). Part-whole relations: some structural features of children's representational block play. Child Care Quarterly, 12(2), 144-151.
219. Rieser, J. J., Garing, A. E., & Young, M. E. (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, 1262-1278.
220. Robert, M., & Héroux, G. (2003). Visuo-spatial play experience: forerunner of visuo-spatial achievement in preadolescent and adolescent boys and girls. Infant and Child Development, 13(1), 49-78.
221. Roth, W.-M. (2001). Gestures: their role in teaching and learning. Review of Educational Research, 71, 365-392.
222. Ruddick, G., & Sainsbury, M. (2008). Comparison of the core primary curriculum in England and those of other high performing countries. London: National Foundation for Educational Research.
223. Russell, B. (1903/2010). Principles of mathematics. London: Routledge.
224. Sacks, O. (1993, May 10). A Neurologist's Notebook: To see and not see. The New Yorker, pp. 59-73.
225. Sagiv, N., Simner, J., Collins, J., Butterworth, B., & Ward, J. (2006). What is the relationship between synaesthesia and visuo-spatial number forms? Cognition, 101, 114-128.
226. St. Clair-Thompson, H. L., Stevens, R., Hunt, A., & Bolder, E. (2010). Improving children's working memory and classroom performance. Educational Psychology, 30, 203-220.
227. Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. New York: Routledge.
228. Sawyer, W. W. (2003). Vision in elementary mathematics. London: Courier Dover Books in Mathematics.
229. Schubring, G. (Ed.). (n.d.). International Journal for the History of Mathematics Education. New York: Teachers College Press. Available from http://www.comap.com/historyjournal
230. 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). Hillsdale, NJ: Erlbaum.
231. Seron, X., Pesenti, M., Noel, M.-P., Deloche, G., & Cornet, J.-A. (1992). Images of numbers, or "when 98 is upper left and 6 sky blue." Cognition, 44(1-2), 159-196.
232. Seung, H. S., & Lee, D. D. (2000). The manifold ways of perception. Science, 290(5500), 2268-2269.
233. Shaki, S., Fischer, M. H., & Petrusic, W. M. (2009). Reading habits for both words and numbers contribute to the SNARC effect. Psychonomic Bulletin and Review, 16(2), 328-331.
234. Sheets-Johnstone, M. (2012). Movement and mirror neurons: a challenging and choice conversation. Phenomenology and the Cognitive Sciences, 11(3), 385-401.
235. Shepard, R. N., & Metzler, J. (1971). Mental rotation of three-dimensional objects. Science, 171, 701-703.
236. Sherin, B. I. (2001). How students invent representations of motion: a genetic account. Journal of Mathematical Behavior, 19, 399-441.
237. Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75, 428-444.
238. Siegler, R. S., & Ramani, G. B. (2008). Playing linear numerical board games promotes low-income children's numerical development. Developmental Science, 11, 655-661.
239. Siegler, R. S., & Ramani, G. B. (2009). Playing linear number board games - but not circular ones - improves low-income preschoolers' numerical understanding. Journal of Educational Psychology, 101, 545-560.
240. SIGGRAPH. (2002). White Paper on Visual Learning in Science and Engineering, report from the Visual Learning Campfire, Snowbird, UT: ACMSIGGRAPH Education Committee, http://education.siggraph.org/conferences/other/visual-learning
241. Sinclair, N. (2008). The history of geometry curriculum in the United States. Charlotte, NC: Information Age Publishing.
242. Sinclair, N. (2014). Motion in mathematics. Keynote address at the British Columbia Association of Mathematics Teachers' Annual Fall Conference. Available at: http://youtube.be/FILJ6FoDLXg
243. Sinclair, N., & Armstrong, A. (2011). Tell a piecewise story. Mathematics Teaching in the Middle School, 16(6), 346-353.
244. Sinclair, N., & Bruce, C. D. (coordinators). (2014). Research forum: Spatial reasoning for young learners. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36, vol. 1 (pp. 173-203). Vancouver, BC: PME.
245. Sinclair, N., & de Freitas, E. (in press). The haptic nature of gesture: rethinking gesture with new multitouch digital technologies. Gesture.
246. Sinclair, N., de Freitas, E., & Ferrara, F. (2013). Virtual encounters: the murky and furtive world of mathematical inventiveness. ZDM: The International Journal on Mathematics Education, 45(2), 239-252.
247. Sinclair, N., & Gol Tabaghi, S. (2010). Drawing space: mathematicians' kinetic conceptions of eigenvectors. Education Studies in Mathematics, 74(3), 223-240.
248. Sinclair, N., & Moss, J. (2012). The more it changes, the more it becomes the same: the development of the routine of shape identification in dynamic geometry environments. International Journal of Education Research, 51&52, 28-44.
249. Sorby, S. A. (2009). Developing spatial cognitive skills among middle school students. Cognitive Processing, 10 (Suppl 2). doi: 10.1007/s10339-009-0310-y
250. Sorby, S. A. (2012). Developing spatial thinking. Clifton Park, NY: Delmar, Cengage Learning.
251. Sorby, S., Casey, B. M., Veurink, N., & Dulaney, A. (2013). The role of spatial training in improving spatial and calculus performance in engineering students. Learning and Individual Differences, 26, 20-29.
252. Spatial Intelligence and Learning Center Tests and Instruments. (2014). Retrieved from http://spatiallearning.org/index/php/testsainstruments
253. Spencer, S. J., Steele, C. M., & Quinn, D. M. (1999). Stereotype threat and women's math performance. Journal of Experimental Social Psychology, 35(1), 4-28.
254. Stanic, G., & Kilpatrick, J. (Eds.). (2003). A history of school mathematics. Reston, VA: National Council of Teachers of Mathematics.
255. 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.
256. Stenning, K. (2002). Seeing reason: image and language in learning to think. Oxford: UK: Oxford University Press.
257. Stevens, R. (2012). The missing bodies of mathematical thinking and learning have been found. Journal of the Learning Sciences, 21(2), 337-346.
258. Stewart, I. (2007). Why beauty is truth: a history of symmetry. New York: Basic Books.
259. Stull, A. T., Barrett, T., & Hegarty, M. (2013). Usability of concrete and virtual models in chemistry instruction. Computers in Human Behavior, 29(6), 2546-2556. doi: 10.1016/j.chb.2013.06.012
260. Stull, A. T., Hegarty, M., Dixon, B., & Stieff, M. (2012). Representational translation with concrete models in organic chemistry. Cognition and Instruction, 30(4), 404-434. doi: 10.1080/07370008.2012.719956
261. Stumpf, H., & Haldimann, M. (1997). Spatial ability and academic success of sixth grade students at international schools. School Psychology International, 18(3), 245-259. doi: 10.1177/0143034397183005
262. Tahta, D. (1980). About geometry. For the Learning of Mathematics, 1(1), 2-9.
263. Tahta, D. (1989). Is there a geometric imperative? Mathematics Teaching, 129, 20-29.
264. Taylor, H. A., & Hutton, A. (2013). Think3dk training spatial thinking fundamental to STEM Education. Cognition and Instruction, 31(4), 434-455.
265. Terlecki, M., Newcombe, N., & Little, M. (2008). Durable and generalized effects of spatial experience on mental rotation: gender differences in growth patterns. Applied Cognitive Psychology, 22, 996-1013.
266. Thom, J. S. (2011). Nurturing mathematical reasoning. Teaching Children's Mathematics, 18(4), 234-243.
267. Thom, J. S. (2012). Re-rooting the learning space: minding where children's mathematics grow. Rotterdam, NL: Sense.
268. Thom, J., & McGarvey, L. (in press). The act and artifact of drawing(s) in mathematics: observing geometric thinking through children's drawings. ZDM: The International Journal on Mathematics Education, 15(3).
269. Thom, J., & Roth, W.-M. (2011). Radical embodiment and semiotics: toward a theory of mathematics in the flesh. Educational Studies in Mathematics, 77, 267-284.
270. Thompson, J., Nuerk, H. C., Moeller, K., & Cohen Kadosh, R. (2013). The link between mental rotation ability and basic numerical representations. Acta Psychologica, 144, 324-331.
271. Thurston, W. (1995). On proof and progress in mathematics. For the Learning of Mathematics, 15(1), 29-37.
272. Thurston, W. P. (1994). On proof and progress in mathematics. The American Mathematical Society, 30(2), pp. 161-177.
273. nd edition. New York: CRC Press.
274. Towers, J., & Martin, L. C. (2014). Enactivism and the study of collectivity. ZDM: The International Journal on Mathematics Education, 47(2). doi: 10.1007/s11858-014-0643-6
275. Trafton, J. G. & Harrison, A. M. (2011). Embodied spatial cognition. Topics in Cognitive Science, 3(4), 686-706.
276. 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.
277. Uttal, D. H. (2000). Seeing the big picture: map use and the development of spatial cognition. Developmental Science, 3(3), 747-286.
278. 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. doi: 10.1037/a0028446
279. Varela, F. J., Thompson, E., & Rosch, E. (1991). The embodied mind: cognitive science and human experience. Cambridge, MA: MIT Press.
280. Vasilyeva, M., & Bowers, E. (2006). Children's use of geometric information in mapping tasks. Journal of Experimental Child Psychology, 95(4), 255-277.
281. Vasilyeva, M., & Huttenlocher, J. (2004). Early development of scaling ability. Developmental Psychology, 40(5), 682-690.
282. Vasta, R., Knott, J. A., & Gaze, C. E. (1996). Can spatial training erase the gender differences on the water-level task?. Psychology of Women Quarterly, 20(4), 549-567.
283. Verdine, B. N., Golinkoff, R. M., Hirsh-Pasek, K., & Newcombe, N. S. (2014). Finding the missing piece: blocks, puzzles, and shapes fuel school readiness. Trends in Neuroscience and Education, 7(1), 7-13. doi.org/10.1016/j.tine.2014.02.005
284. Verdine, B. N., Golinkoff, R., Hirsh-Pasek, K., Newcombe, N., Filipowocz, A. T., & Chang, A. (2014). Deconstructing building blocks: preschoolers' spatial assembly performance relates to early mathematics skills. Child Development, 85(3), 1062-1076. doi: 10.1111/cdev.12165
285. Verdine, B. N., Troseth, G. L., Hodapp, R. M., & Dykens, E. M. (2008). Strategies and correlates of jigsaw puzzle and visuospatial performance by persons with prader-willi syndrome. American Journal of Mental Retardation, 113(5), 343-355.
286. Voyer, D. (2011). Time limits and gender differences on paper-and-pencil tests of mental rotation: a meta-analysis. Psychonomic Bulletin & Review, 18(2), 267-277.
287. Vygotsky, L. S., & Luria, A. (1993). Studies on the history of behavior, ape, primitive, and child. Hillsdale, NJ: Lawrence Erlbaum Associates.
288. 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.
289. Watters, E. (2013). We aren't the world. Retrieved from http://www.psmag.com/magazines/magazine-feature-story-magazines/joe-henrich-weird-ultimatum-game-shaking-up-psychology-economics-53135/
290. Werner, K., & Raab, M. (2014). Moving your eyes to solution: effects of movements on the perception of a problem-solving task. The Quarterly Journal of Experimental Psychology, 67(8), 1571-1578.
291. Wheatley, G. (1996). Quick draw: Developing spatial sense in mathematics. Tallahassee: Florida Department of Education.
292. th-century North America. Proceedings of the Annual Meeting of the Canadian Mathematics Education Study Group. http://www.math.yorku.ca/~whiteley/cmesg.pdf
293. Whiteley, W. (2005). Learning to see like a mathematician. In G. Malcolm (Ed.), Multidisciplinary approaches to visual representation and interpretation (pp. 279-292). New York: Elsevier.
294. Whiteley, W., & Mamolo, A. (2014). Optimizing through geometric reasoning supported by 3D models: visual representations of change. In A. Watson & M. Ohtani (Eds.), ICMI Study 22 on Task Design (pp. 129-140). Berlin: Springer.
295. th International Congress on Mathematics Education (ICME 11), Monterrey, MX, July.
296. Wikipedia. (2014a). Multiview orthographic projection. Retrieved August 31, 2014, from http://en.wikipedia.org/wiki/Multiview_orthographic_projection
297. Wikipedia. (2014b). Chirality in Chemistry. Retrieved October 31, 2014, from http://en.wikipedia.org/wiki/Chirality_(chemistry)
298. Wikipedia. (2014c). Necker Cube. Retrieved October 31, 2014, from http://en.wikipedia.org/wiki/Necker_cube
299. Witkin, H. A. (1971). A manual for the embedded figures tests. Palo Alto, CA: Consulting Psychologists Press.
300. Witkin, H. A., & Asch, S. E. (1948). Studies in space orientation: IV. Further experiments on perception of the upright with displaced visual fields. Journal of Experimental Psychology, 38, 762-782.
301. Witt, M. (2011). School based working memory training: preliminary finding of improvement in children's mathematical performance. Advances in Cognitive Psychology, 7(1), 7-15. doi: 10.2478/v10053-008-0083-3
302. Wolfgang, C. H., Stannard, L. L., & Jones, I. (2001). Block play performance among preschoolers as a predictor of later school achievement in mathematics. Journal of Research in Childhood Education, 15(2), 173-180.
303. Wright, R., Thompson, W., Ganis, G., Newcombe, N., & Kosslyn, S. (2008). Training generalized spatial skills. Psychonomic Bulletin and Review, 15(4), 763-771.
304. Zimmermann, W. (1991). Visual thinking in calculus. In W. Zimmermann & S. Cunningham (Eds.), Visualization in teaching and learning mathematics (pp. 127-137). Washington, DC: Mathematical Association of America.