Skip to main content

Visuospatial Reasoning in Twentieth Century Psychology-Based Studies

  • Chapter
  • First Online:
Visuospatial Reasoning

Part of the book series: Mathematics Education Library ((MELI,volume 111))

  • 1230 Accesses

Abstract

A critical literature review of psychology studies on spatial abilities and visual imagery especially those that linked with mathematics education is synthesised. Most of the literature is from an era last century when visuospatial reasoning (under the names of spatial abilities, visual imagery, and visual processing) was high on the research agenda. However, more recent studies are also included along with the concern that its importance has been forgotten under national testing regimes. Based on the literature review, a key classroom study demonstrated the diversity of visuospatial reasoning within the context of the classroom. The effectiveness of specific learning experiences focussing on visuospatial reasoning for geometry illustrated the importance of developing pictorial, dynamic, pattern, and action visuospatial reasoning. In particular, the problem-solving nature of the learning experiences showed how the mathematics learner attends to objects (mental and physical) and people, and uses visuospatial reasoning along with other cognitive processes, heuristics, and affect. As a result, the learner’s responsiveness provides a way forward in problem solving. Responsiveness in turn influences the immediate context forming a cycle of learning. By unpacking the studies to focus on visuospatial reasoning by “getting inside children’s heads”, it was shown how early geometry learning should focus on investigating, visualising, describing, and classifying with an emphasis on the concepts associated with parts and wholes of shapes and on orientation and motion of and within shapes. Subsequent studies in schools confirmed the effectiveness for visuospatial reasoning and geometry learning. However, the need for a closer recognition of cultural difference was becoming more apparent.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    This study and my own were undertaken in Australia where in fact grades are called Year 1, Year 2, etc. but grade is used here for consistency with other countries.

  2. 2.

    All children participated in an introductory lesson, so the kind of interactive behaviour expected in investigations was established and children and I came to know each other. The class teacher taught the other half of the class and then we swapped.

  3. 3.

    Tangram sets were made from cardboard with three sizes of right-angled isosceles triangles (two large, two small, and one medium), a parallelogram, and a square which combine to make a square. This is a well-known puzzle that can be used to make many shapes and pictures and the shapes have special relationships, e.g. the square, parallelogram, and medium triangle can all be made from two small triangles.

  4. 4.

    Grade 2 started with four squares; square breadclips were used.

  5. 5.

    Foam sets were used consisting of an equilateral triangle, an isosceles trapezium (equal to three triangles), a square, two sizes of rhombus, one of which is equal to two triangles, and a regular hexagon (equal to six triangles), a readily available set.

  6. 6.

    Angles of shapes were marked by the thumb and forefinger to show size. The forefinger is rotated to line along the other arm of the angle.

  7. 7.

    Each shape was printed on paper.

  8. 8.

    Each shape was made from cardboard and a number given in each packet. Packets were swapped between children.

  9. 9.

    John Conroy, a retired mathematics educator from Macquarie University assisted with videotaping. All children were taught by myself. Lapel microphones were attached to children. To avoid class disruptions half the class working individually were taught followed by half the class working in groups on number or space problems.

  10. 10.

    The videorecorded actions and interactions were described and spoken words recorded. An incident was a small self-contained segment of learning that could be described. After analysis, these tended to be a small cycle (context, context providing input, child or children’s thinking, response affecting context), many of which formed a cycle within learning. (See Fig. 2.17 on responsiveness in problem solving towards end of this study.)

  11. 11.

    All names are pseudonyms.

  12. 12.

    Presmeg (1986) referred to dynamic imagery as involving movement in remembering formulae such as moving letters in expanding a product of two binomials.

  13. 13.

    Presmeg (1986) used the term “pattern imagery” and illustrated it with symbolic and numeral patterns.

References

  • Abe, K., & Del Grande, J. (1983). Geometric activities in the elementary school. In M. Zweng, T. Green, J. Kilpatrick, H. Pollak, & M. Suydam (Eds.), Proceedings of the Fourth International Congress on Mathematical Education (pp. 161–164). Boston: Birkhauser.

    Google Scholar 

  • Allport, D. (1987). Selection for action: Some behavioral and neurophysiological considerations of attention and action. In H. Heuer & A. Sanders (Eds.), Perspectives on perception and action (pp. 395–420). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Anderson, R. (1978). Arguments concerning representations for mental imagery. Psychological Review, 85(4), 249–277.

    Google Scholar 

  • Aust, R. (1989). Constructing mental representations of complex three-dimensional objects. Lawrence, KS: University of Kansas.

    Google Scholar 

  • Baddeley, A. (1992). Working memory. Science, 255, 395–406.

    Google Scholar 

  • Baenninger, M., & Newcombe, N. S. (1989). The role of experience in spatial test performance: A meta-analysis. Sex Roles, 20(5/6), 327–344.

    Google Scholar 

  • Barratt, E. S. (1953). An analysis of verbal reports of solving spatial problems as an aid in defining spatial factors. Journal of Psychology, 36, 17–25.

    Google Scholar 

  • Bauersfeld, H. (1991). The structuring of the structures: Development and function of mathematizing as a social practice. In L. Steffe (Ed.), Constructivism and education (pp. 1–26). Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Bellugi, U., Sabo, H., & Vaid, J. (1988). Spatial deficits in children with Williams Syndrome. In J. Stiles-Davis, M. Kritchevsky, & U. Bellugi (Eds.), Spatial cognition: Brain bases and development (pp. 273–298). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Ben-Chaim, D., Lappan, G., & Houang, R. (1988). The effect of instruction on spatial visualization skills by middle school boys and girls. American Educational Research Journal, 25, 51–71.

    Google Scholar 

  • Bishop, A. (1973). Structural apparatus and spatial ability. Research in Education, 9, 43–49.

    Google Scholar 

  • Bishop, A. (1983). Space and geometry. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 176–204). New York: Academic Press.

    Google Scholar 

  • Bishop, A. (1988). Mathematical enculturation: A cultural perspective on mathematics education. Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Booth, D. (1994). Art and geometry learning through spontaneous pattern making. Journal of Institute of Art Education, 9(2), 28–42.

    Google Scholar 

  • Bruner, J. (1964). The course of cognitive growth. American Psychologist: Anthropology and Education, 19, 1–15.

    Google Scholar 

  • Burden, L., & Coulson, S. (1981). Processing of spatial tasks. Masters thesis, Monash University, Melbourne, Australia.

    Google Scholar 

  • Campbell-Jones, S. (1996). Horizon: Twice five plus the wings of a bird. London, UK: BBC.

    Google Scholar 

  • Carpenter, P., & Just, M. (1986). Spatial ability: An information processing approach to psychometrics. In R. J. Sternberg (Ed.), Advances in the psychology of human intelligence (Vol. 3, pp. 221–253). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Cheng, K., Huttenlocher, J., & Newcombe, N. (2013). 25 years of research on the use of geometry in spatial reorientation: A current theoretical perspective. Psychonomic Bulletin & Review, 20(6), 1033–1054.

    Google Scholar 

  • Civil, M., & Andrade, R. (2002). Transitions between home and school mathematics: Rays of hope amidst the passing clouds. In G. De Abreu, A. Bishop, & N. Presmeg (Eds.), Transitions between contexts of mathematical practices (pp. 148–168). Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Clements, M. (1983). The question of how spatial ability is defined, and its relevance to mathematics education. Zentralblatt fur Didaktik der Mathematik, 1(1), 8–20.

    Google Scholar 

  • Clements, M. (2012). A historical overview of visualisation and visualising in mathematics education. Paper presented at the Retirement Symposium of Ted Eisenberg, Israel.

    Google Scholar 

  • Clements, D., Battista, M., & Sarama, J. (1998). Development of geometric and measurement ideas. In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 201–226). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Clements, D., & Sarama, J. (2007). Early childhood mathematics learning. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 479–530, especially 488–530). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Clements, D., & Sarama, J. (2007). Effects of a preschool mathematics curriculum: Summative research on the Building Blocks project. Journal for Research in Mathematics Education, 38, 136–163.

    Google Scholar 

  • Clements, D., Wilson, D., & Sarama, J. (2004). Young children’s composition of geometric figures: A learning trajectory. Mathematical Thinking and Learning, 6, 163–184.

    Google Scholar 

  • Cooper, L., & Shepard, R. (1973). Chronometric studies of the rotation of mental images. In W. Chase (Ed.), Visual information processing (pp. 76–176). New York: Academic Press.

    Google Scholar 

  • Cox, M. (1978). Perspective ability: A training programme. Journal of Educational Research, 71, 127–133.

    Google Scholar 

  • Del Campo, G., & Clements, M. (1990). Expanding the modes of communication in mathematics classrooms. Journal fur Mathematik-Didaktik, 11, 45–79.

    Google Scholar 

  • Del Grande, J. (1990). Spatial sense. Arithmetic Teacher, 27, 14–20.

    Google Scholar 

  • Del Grande, J. (1992). Geometry and spatial abilities. Paper presented at the Subgroup 11.1: Geometry as a Part of Education in Early Childhood in Working Group 11: The Role of Geometry in General Education. International Congress on Mathematical Education, ICME 7, Quebec.

    Google Scholar 

  • Deregowski, J. B. (1980). Illusions, patterns and pictures: A cross-cultural perspective. London: Academic Press.

    Google Scholar 

  • Dörfler, W. (2004). Mathematical reasoning: Mental activity or practice with diagrams. Paper presented at the International Congress on Mathematics Education ICME11, Denmark. Retrieved from http://www.icme10.dk/proceedings/pages/regular_pdf/RL_Willi_Doerfler.pdf

  • Dreyfus, T. (1991). On the status of visual reasoning in mathematics and mathematics education. In F. Furinghetti (Ed.), 15th PME Conference (Vol. 1, pp. 33–48). Italy: Program Committee for the International Group for the Psychology of Mathematics Education.

    Google Scholar 

  • Egan, D. E. (1979). Testing based on understanding: Implications from studies of spatial ability. Intelligence, 3, 1–15.

    Google Scholar 

  • Egan, K. (1992). Imagination in teaching and learning: Ages 8 to 15. London: Routledge.

    Google Scholar 

  • Eliot, J. (1987). Models of psychological space: Psychometric, developmental, and experimental approaches. New York: Springer.

    Google Scholar 

  • Eliot, J., & McFarlane-Smith, I. (1983). International directory of spatial tests. Windsor: NRER-Nelson.

    Google Scholar 

  • English, L. (1994). Reasoning by analogy in constructing mathematical ideas. In G. Bell, B. Wright, N. Leeson, & J. Geake (Eds.), Challenges in mathematics education: Constraints on Construction (pp. 213–222). Lismore: Mathematics Education Group of Australasia.

    Google Scholar 

  • Farnham-Diggory, S. (1967). Symbol and synthesis in experimental “reading”. Child Development, 38(1), 221–231.

    Google Scholar 

  • Fennema, E. (1984). Girls, women, and mathematics: An overview. In E. Fennema & J. Ayer (Eds.), Women and education: Equity or equality (pp. 137–164). Berkeley, CA: McCutchan.

    Google Scholar 

  • Flavell, J. (1977). Cognitive development. Englewood Cliffs, NJ: Prentice-Hall.

    Google Scholar 

  • Flavell, J. (1987). Speculations about the nature and development of metacognition. In F. Weinert & R. Kluwe (Eds.), Metacognition, motivation, and understanding (pp. 21–29). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Flores, A. (1995). Bilingual lessons in the early-grades. Teaching Children Mathematics, 1(7), 420–424.

    Google Scholar 

  • Frostig, M., & Horne, D. (1964). The Frostig program for the development of visual perception. Chicago: Follett.

    Google Scholar 

  • Fuson, K., & Murray, C. (Eds.). (1978). The haptic-visual perception, construction, and drawing of geometric shapes by children aged two to five: A Piagetian extension. Columbus, Ohio: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

    Google Scholar 

  • Gagné, R., & White, R. (1978). Memory structures and learning outcomes. Review of Educational Research, 48(2), 187–222.

    Google Scholar 

  • Gell, A. (1998). Art and agency: An anthropological theory. Oxford: Clarendon Press.

    Google Scholar 

  • Genkins, E. (1975). The concept of bilateral symmetry in young children. In M. Rosskopf (Ed.), Children’s mathematical concepts: Six Piagetian studies in mathematics education (pp. 5–43). Columbia, NY: Teachers College Press.

    Google Scholar 

  • Giaquinto, M. (2011). Visual thinking in mathematics: An epistemological study. Oxford: Oxford University Press.

    Google Scholar 

  • Gibson, J. (1979). The ecological approach to visual perception. Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Goldenberg, P., & Mason, J. (2008). Shedding light on and with example spaces. Educational Studies in Mathematics, 69(2), 183–194. doi:10.1007/s10649-008-9143-3.

    Google Scholar 

  • Goldin, G. (Ed.). (1987). (a) Levels of language in mathematical problem solving; (b) Cognitive representational systems for mathematical problem solving. Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Goldin, G. (1998). The PME Working Group on Representation. Journal of Mathematical Behavior, 17(2), 283–301.

    Google Scholar 

  • Gray, E., & Tall, D. (2007). Abstraction as a natural process of mental compression. Mathematics Education Research Journal, 19(2), 23–40.

    Google Scholar 

  • Gutstein, E. (2006). Reading and writing the world with mathematics: Towards a pedagogy for social justice. New York: Routledge.

    Google Scholar 

  • Healy, L., & Fernandes, S. (2011). The role of gestures in the mathematical practices of those who do not see with their eyes. Educational Studies in Mathematics, 77(2), 157–174. doi:10.1007/s10649-010-9290-1.

    Google Scholar 

  • Healy, L., & Powell, A. (2013). Understanding and overcoming “disadvantage” in learning mathematics. In M. Clements, A. Bishop, C. Keitel, J. Kilpatrick, & F. Leung (Eds.), Third international handbook of mathematics education (Springer International Handbooks of Education). New York: Springer.

    Google Scholar 

  • Hegarty, M., & Kozhevnikov, M. (1999). Types of visual–spatial representations and mathematical problem solving. Journal of Educational Psychology, 91(4), 684–689.

    Google Scholar 

  • Hershkowitz, R. (1989). Visualization in geometry—Two sides of the coin. Focus on Learning Problems in Mathematics, 11(1), 61–76.

    Google Scholar 

  • Hershkowitz, R. (1990). Psychological aspects of learning geometry. In P. Nesher & J. Kilpatrick (Eds.), Mathematics and cognition: A research synthesis by the International Group for the Psychology of Mathematics Education (pp. 70–95). Cambridge: Cambridge University Press.

    Google Scholar 

  • Johnson, M. (1987). The body and the mind: The bodily basis of meaning, imagination, and reason. Chicago: University of Chicago Press.

    Google Scholar 

  • Johnson, E., & Meade, A. (1985). The JM battery of spatial tests: Lower battery.

    Google Scholar 

  • Johnston, W., & Heinz, S. (1978). Flexibility and capacity demands of attention. Journal of Experimental Psychology, General, 107, 420–435.

    Google Scholar 

  • Kahneman, D. (1973). Attention and effort. Englemwood Cliffs, NJ: Prentice-Hall.

    Google Scholar 

  • Kaufmann, G. (1979). Visual imagery and its relation to problem solving. Bergen: Universitetsforlaget.

    Google Scholar 

  • Kieras, D. (1978). Beyond pictures and words: Alternative information processing models for imagery effects in verbal memory. Psychological Bulletin, 85, 532–554.

    Google Scholar 

  • Kim, M., Roth, W.-M., & Thom, J. (2011). Children’s gestures and the embodied knowledge of geometry. International Journal of Science and Mathematics Education, 9, 207–238.

    Google Scholar 

  • Kosslyn, S. (1981). The medium and message in mental imagery: A theory. Psychological Review, 88(1), 46–66.

    Google Scholar 

  • Kosslyn, S. (1983). Ghosts in the mind’s machine. New York: W.W. Norton.

    Google Scholar 

  • Kosslyn, S., & Pomerantz, J. (1977). Imagery, propositions and the form of internal representations. Cognitive Psychology, 7, 341–370.

    Google Scholar 

  • Kritchevsky, M. (1988). The elementary spatial functions of the brain. In J. Stiles-Davis, M. Kritchevsky, & U. Bellugi (Eds.), Spatial cognition: Brain bases and development (pp. 111–139). Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Krutetskii, V. (1976). The psychology of mathematical abilities in schoolchildren. In J. Kilpatrick & I. Wirszup (Eds.), Soviet studies in the psychology of learning and teaching mathematics. Survey of recent East European mathematical literature (Vol. II: The structure of mathematical abilities, pp. 5–58). Chicago: University of Chicago.

    Google Scholar 

  • Kurina, F. (1992). Geometry in the early childhood education. Paper presented at the Subgroup 11.1: Geometry as a Part of Education in Early Childhood in Working Group 11: The Role of Geometry in General Education. International Congress on Mathematical Education, ICME 7, Quebec.

    Google Scholar 

  • Kyllonen, P. C., Lohman, D. F., & Snow, R. E. (1984). Effects of aptitudes, strategy training, and task facets on spatial task performance. Journal of Educational Psychology, 76(1), 130–145.

    Google Scholar 

  • Laborde, C., Kynoigos, C., Hollebrands, K., & Strässer, R. (2006). Teaching and learning geometry with technology. In A. Gutiérrez & P. Boera (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future. Rotterdam: Sense Publishers.

    Google Scholar 

  • Lakoff, G. (1987). Women, fire, and dangerous things: What categories reveal about the mind. Chicago: University of Chicago Press.

    Google Scholar 

  • Landau, B. (1988). The construction and use of spatial knowledge in blind and sighted children. In J. Stiles-Davis, M. Kritchevsky, & U. Bellugi (Eds.), Spatial cognition: Brain bases and development (pp. 343–372). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Lean, G. (1984). The conquest of space: A review of the research literatures pertaining to the development of spatial abilities underlying an understanding of 3-D geometry. Paper presented at the Fifth International Congress on Mathematical Education, Adelaide, Australia.

    Google Scholar 

  • Lean, G., & Clements, M. (1981). Spatial ability, visual imagery, and mathematical performance. Educational Studies in Mathematics, 12, 267–299.

    Google Scholar 

  • Learmonth, A. E., Newcombe, N. S., Sheridan, N., & Jones, M. (2008). Why size counts: Children’s spatial reorientation in large and small enclosures. Developmental Science, 11(3), 414–426.

    Google Scholar 

  • 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). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Leinhardt, G., Zaslavsky, O., & Stein, M. (1990). Functions, graphs, and graphing: Tasks, learning and teaching. Review of Educational Research, 60(1–64).

    Google Scholar 

  • Lester, F. (Ed.). (1983). Trends and issues in mathematical problem-solving research. New York: Academic Press.

    Google Scholar 

  • Lévi-Strauss, C. (1968). The savage mind. Chicago: University of Chicago Press.

    Google Scholar 

  • Lillo-Martin, D., & Tallal, P. (1988). Effects of different early experiences. In J. Stiles-Davis, M. Kritchevsky, & U. Bellugi (Eds.), Spatial cognition: Brain bases and development (pp. 433–441). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Linn, M., & Hyde, J. (1989). Gender, mathematics, and science. Educational Researcher, 18(8), 17–19. 22–27.

    Google Scholar 

  • Liu, Y., & Wickens, C. (1992). Visual scanning with or without spatial uncertainty and divided and selective attention. Acta Psychologica, 79, 139–153.

    Google Scholar 

  • Lohman, D. F. (1979). Spatial ability: A review and re-analysis of the correlational literature (Technical Report No. 8). Stanford, CA: Aptitude Research Project, Stanford University School of Education.

    Google Scholar 

  • Lohman, D. F., Pellegrino, J. W., Alderton, D. L., & Regian, J. W. (1987). Dimensions and components of individual differences in spatial abilities. In S. H. Irvine & S. E. Newstead (Eds.), Intelligence and cognition (pp. 253–312). Dordrecht, The Netherlands: Nijhoff Publishers.

    Google Scholar 

  • Lowrie, T. (1992). Developing talented children’s mathematical ability through visual and spatial learning tasks. Paper presented at the Annual Conference of the Australian Association for Research in Education, Deakin University, Geelong, VIC, Australia.

    Google Scholar 

  • Lowrie, T., Logan, T., & Scriven, B. (2012). Perspectives on geometry and measurement in the Australian Curriculum: Mathematics. In B. Atweh, M. Goos, R. Jorgensen, & D. Siemon (Eds.), Engaging the Australian National Curriculum: Mathematics—Perspectives from the field (Online Publication) (pp. 71–88). Adelaide, SA, Australia: Mathematics Education Research Group of Australasia.

    Google Scholar 

  • Magoon, R., & Garrison, K. (1976). Educational psychology: An integrated view (2nd ed.). Columbus, OH: Charles E. Merrill.

    Google Scholar 

  • Mandler, J. (1988). The development of spatial cognition: On topological and Euclidean representation. In J. Stiles-Davis, M. Kritchevsky, & U. Bellugi (Eds.), Spatial cognition: Brain bases and development (pp. 423–432). Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Martlew, M., & Connolly, K. (1996). Human figure drawings by schooled and unschooled children in Papua New Guinea. Child Development, 67(6), 2743–2762. doi:10.1111/j.1467-8624.1996.tb01886.x.

    Google Scholar 

  • Mason, J. (2003). Structure of attention in the learning of mathematics. In J. Novotná (Ed.), Proceedings of the International Symposium on Elementary Mathematics Teaching (pp. 9–16). Prague: Charles University.

    Google Scholar 

  • McGee, M. (1979). Human spatial abilities: Psychometric studies; Environmental, genetic, hormonal, and neurological influences. Psychological Bulletin, 89, 889–918.

    Google Scholar 

  • Michael, W., Guilford, J., Fruchter, B., & Zimmerman, W. (1957). Description of spatial visualization abilities. Educational and Psychological Measurement, 17, 185–199.

    Google Scholar 

  • Mildren, J. (1990). The elegant path to metacognition. In M. A. Clements (Ed.), Whither Mathematics? Proceedings of the 27th Annual Conference of The Mathematical Association of Victoria (pp. 373–379). Melbourne: The Mathematical Association of Victoria.

    Google Scholar 

  • Moses, B. (1977). The nature of spatial ability and its relationship to mathematical problem solving. Ph.D. thesis, Indiana University.

    Google Scholar 

  • Neville, H. (1988). Cerebral organization for spatial attention. In J. Stiles-Davis, M. Kritchevsky, & U. Bellugi (Eds.), Spatial cognition: Brain bases and development (pp. 327–342). Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Newcombe, N., & Huttenlocher, J. (2000). Making space: The development of spatial representation and reasoning. Cambridge, MA: MIT Press.

    Google Scholar 

  • NSW Department of Education and Training. (1998). Count Me In Too. Retrieved from http://www.curriculumsupport.education.nsw.gov.au/primary/mathematics/countmeintoo/index.htm

  • NSW Department of Education and Training Curriculum Support and Development. (2000). Count Me Into Space. Resource for teachers with learning framework, exemplar lessons, assessment tasks, three videorecordings. Sydney: Author.

    Google Scholar 

  • Osborne, R., & Wittrock, M. (1983). Learning science: A generative process. Science Education, 67, 489–508.

    Google Scholar 

  • Outhred, L. (1993). The development in young children of concepts of rectangular area measurement. Doctoral thesis, Macquarie University, Sydney.

    Google Scholar 

  • Owens, K. (1990). Getting inside the problem solver’s head: Using retrospection and observation to access spatial and problem thinking processes. Paper presented at the 13th Annual Conference of the Mathematics Education Research Group of Australasia MERGA13, Hobart.

    Google Scholar 

  • Owens, K. (1992a). Spatial mathematics: A group test for primary school students. In K. Stephens & J. Izard (Eds.), Reshaping assessment practices: Assessment in the mathematical sciences under challenge. Melbourne: Australian Council for Education Research.

    Google Scholar 

  • Owens, K. (1993). Spatial thinking processes employed by primary school students engaged in mathematical problem solving. Ph.D. thesis, Deakin University, Geelong, Victoria, Australia. Retrieved from http://dro.deakin.edu.au/eserv/DU:30023339/owens-spatialthinking-1993.pdf informit database.

  • Owens, K. (1996b). Recent research and a critique of theories of early geometry learning: The case of the angle concept. Nordisk Matematikk Didaktikk-Nordic Studies in Mathematics Education, 4(2/3), 85–106.

    Google Scholar 

  • Owens, K. (1997a). Classroom views of space. In B. Doig & J. Lokan (Eds.), Learning from children: Mathematics from a classroom perspective (pp. 125–146). Melbourne: Australian Council for Educational Research.

    Google Scholar 

  • Owens, K. (1998a). Explaining spatial problem solving in terms of cognitive load or responsiveness and selective attention. In P. Jeffery (Ed.), Annual Conference of Australian Association for Research in Education. File: Owe98243. Melbourne: AARE.

    Google Scholar 

  • Owens, K. (2001a). Development of the test: Thinking about 3D Shapes. Sydney: NSW Department of Education and Training.

    Google Scholar 

  • Owens, K. (2001c). The work of Glendon Lean on the counting systems of Papua New Guinea and Oceania. Mathematics Education Research Journal, 13(1), 47–71.

    Google Scholar 

  • Owens, K. (2002a). Count Me Into Space implementation over two years with consultancy support. NSW Department of Education and Training Professional Support and Curriculum Directorate.

    Google Scholar 

  • Owens, K. (2002b). Final report on Count Me Into Space with school-based facilitators. Sydney, Australia: NSW Department of Education and Training Professional Support and Curriculum Division.

    Google Scholar 

  • Owens, K. (2002c). Report on Count Me Into Space implemented in 2001 by two groups of schools using facilitators from the schools. NSW Department of Education and Training Professional Support and Curriculum Directorate.

    Google Scholar 

  • Owens, K. (2004a). Imagery and property noticing: Young students’ perceptions of three-dimensional shapes. In P. Jeffery (Ed.), Proceedings of the Annual Conference for the Australian Association for Research in Education. AARE: Melbourne, Australia. Retrieved from http://www.aare.edu.au/conf04/. File: OWE04038.

    Google Scholar 

  • Owens, K. (2004b). Improving the teaching and learning of space mathematics. In B. Clarke, D. Clarke, G. Emanuelsson, B. Johansson, D. Lambdin, F. Lester, A. Wallby, & K. Wallby (Eds.), International perspectives on learning and teaching mathematics (pp. 569–584). Gothenburg, Sweden: Göteborg University National Center for Mathematics Education.

    Google Scholar 

  • Owens, K. (2006a). Creating space Professional knowledge and spatial activities for teaching mathematics. Retrieved from http://athene.riv.csu.edu.au/~kowens/creatingspaceit.

    Google Scholar 

  • Owens, K., & Clements, M. (1998). Representations used in spatial problem solving in the classroom. Journal of Mathematical Behavior, 17(2), 197–218.

    Google Scholar 

  • Owens, K., & Outhred, L. (1996). Young children’s understandings of tiling areas. Reflections, 21(3), 35–40.

    Google Scholar 

  • Owens, K., & Outhred, L. (1997). Early representations of tiling areas. In E. Pehkonen (Ed.), 21st Annual Conference of International Group for Psychology of Mathematics Education (Vol. 3, pp. 312–319). Lahti, Finland: Research and Training Institute & University of Helsinki.

    Google Scholar 

  • Owens, K., & Outhred, L. (1998). Covering shapes with tiles: Primary students’ visualisation and drawing. Mathematics Education Research Journal, 10(3), 28–41.

    Google Scholar 

  • Owens, K., & Outhred, L. (2006). The complexity of learning geometry and measurement. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 83–115). Rotterdam, The Netherlands: Sense Publishers.

    Google Scholar 

  • Owens, K., Perry, B., Conroy, J., Geoghegan, N., & Howe, P. (1998). Responsiveness and affective processes in the interactive construction of understanding in mathematics. Educational Studies in Mathematics, 35(2), 105–127.

    Google Scholar 

  • Owens, K., & Reddacliff, C. (2002). Facilitating the teaching of space mathematics: An evaluation. Paper presented at the Mathematics Education in the South Pacific, 25th Annual Conference of Mathematics Education Research Group of Australasia, Auckland.

    Google Scholar 

  • Owens, K., & Students. (2007). The reality of intellectual quality in the mathematics classroom. Paper presented at the Australian Association of Mathematics Teachers, Hobart.

    Google Scholar 

  • Paivio, A. (1971). Imagery and verbal processing. New York: Holt, Reinhart, & Winston.

    Google Scholar 

  • Paivio, A. (1986). Mental representations: A dual coding approach. New York: Oxford University Press.

    Google Scholar 

  • Pellegrino, J. W., & Hunt, E. B. (1991). Cognitive models for understanding and assessing spatial abilities. In H. Rowe (Ed.), Intelligence: Reconceptualization and measurement. Hillsdale, NJ: Lawrence Erlbaum and Australian Council for Educational Research.

    Google Scholar 

  • 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 (Ed.), Recent research concerning the development of spatial and geometric concepts (pp. 229–242). Columbus, OH: ERIC.

    Google Scholar 

  • Piaget, J., & Inhelder, B. (1956). The child’s conception of space. London: Routledge & Kegan Paul.

    Google Scholar 

  • Piaget, J., & Inhelder, B. (1971). Mental imagery in the child: A study of the development of imaginal representation. London: Routledge & Kegan Paul.

    Google Scholar 

  • Piaget, J., Inhelder, B., & Szeminska, A. (1960). The child’s conception of geometry. New York: Basic Books.

    Google Scholar 

  • Pinxten, R., & François, K. (2011). Politics in an Indian canyon? Some thoughts on the implications of ethnomathematics. Educational Studies in Mathematics, 78(2), 261–273. doi:10.1007/s10649-011-9328-z.

    Google Scholar 

  • Pinxten, R., van Dooren, I., & Harvey, F. (1983). The anthropology of space: Explorations into the natural philosophy and semantics of the Navajo. Philadelphia: University of Pennsylvania Press.

    Google Scholar 

  • Pirie, S., & Kieren, T. (1991). Folding back: Dynamics in the growth of mathematical understanding. In F. Furinghetti (Ed.), Proceedings of the 15th Annual Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 169–176). Italy: Program Committee for the International Group for the Psychology of Mathematics Education.

    Google Scholar 

  • Poltrock, S., & Agnoli, F. (1986). Are spatial visualization ability and visual imagery ability equivalent? In R. J. Sternberg (Ed.), Advances in the psychology of human intelligence (Vol. 3, pp. 255–296). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Poltrock, S., & Brown, P. (1984). Individual differences in visual imagery and spatial ability. Intelligence, 8, 93–138.

    Google Scholar 

  • Presmeg, N. (1986). Visualisation in high school mathematics. For the Learning of Mathematics, 6(3), 42–46.

    Google Scholar 

  • Presmeg, N. (1997). Reasoning with metaphors and metonymies in mathematics learning. In L. English (Ed.), Mathematical reasoning: Analogies, metaphors, and images (pp. 267–279). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Presmeg, N. (2006). Research on visualization in learning and teaching mathematics. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education (pp. 205–304). Rotterdam: Sense Publishers.

    Google Scholar 

  • Pylyshyn, Z. (1979). The rate of “mental rotation” of images: A test of a holistic analogue hypothesis. Memory and Cognition, 7(1), 19–28.

    Google Scholar 

  • Pylyshyn, Z. (1981). The imagery debate: Analogue media versus tacit knowledge. Psychological Review, 88, 16–45.

    Google Scholar 

  • Quinn, M. (1984). Visualization in learning mathematics. Ph.D. thesis, Monash University, Melbourne, Australia.

    Google Scholar 

  • Reisman, F., & Kauffman, S. (1980). Teaching mathematics to children with special needs. Columbus, OH: Merrill.

    Google Scholar 

  • Rivera, F. (2011). Towards a visually-oriented school mathematics classrooms: Research, theory, practice, and issues. New York: Springer.

    Google Scholar 

  • Rosser, R., Lane, S., & Mazzeo, J. (1988). Order of acquisition of related geometric competencies in young children. Child Study Journal, 18(2), 75–89.

    Google Scholar 

  • Rowe, M. (1982). Teaching in spatial skills requiring two- and three-dimensional thinking and different levels of internalization and the retention and transfer of these skills. Melbourne, Australia: Monash University.

    Google Scholar 

  • Saunderson, A. (1973). The effect of a special training programme on spatial ability test performance. New Guinea Psychologists, 5, 13–23.

    Google Scholar 

  • Saxe, G. (2012). Cultural development of mathematical ideas: Papua New Guinea studies. New York: Cambridge University Press.

    Google Scholar 

  • Sheckels, M., & Eliot, J. (1983). Preference and solution patterns in mathematics performance. Perceptual and Motor Skills, 57, 811–816.

    Google Scholar 

  • Shepard, R. (1971). Mental rotation of three dimensional objects. Science, 171, 701–703.

    Google Scholar 

  • Shepard, R. (1975). Form, formation, and transformation of internal representations. In R. Solso (Ed.), Information processing and cognition: The Loyola Symposium (pp. 87–122). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Shepard, R. (1988). The role of transformations in spatial cognition. In J. Stiles-Davis, M. Kritchevsky, & U. Bellugi (Eds.), Spatial cognition: Brain bases and development (pp. 81–110). Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Skemp, R. (1989). Mathematics in the primary schools. London: Routledge.

    Google Scholar 

  • Steffe, L. (Ed.). (1991). Epistemological foundations of mathematical experience. New York: Springer.

    Google Scholar 

  • Stiles-Davis, J., Kritchevsky, M., & Bellugi, U. (Eds.). (1988). Spatial cognition: Brain bases and development. Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Suwarsono, S. (1982). Visual imagery in the mathematical thinking of seventh grade students. Ph.D. thesis, Monash University, Melbourne, Victoria.

    Google Scholar 

  • Sweller, J., & Chandler, P. (1991). Evidence for cognitive load theory. Cognition and Instruction, 8, 351–362.

    Google Scholar 

  • Tartre, L. (1990a). Spatial skills, gender, and mathematics. In E. L. Fennema & G. Leder (Eds.), Mathematics and gender. New York: Teachers College Press.

    Google Scholar 

  • Tartre, L. (1990b). Spatial orientation skill and mathematical problem solving. Journal for Research in Mathematics Education, 21, 216–229.

    Google Scholar 

  • Téllez, K., Moschkovich, J., & Civil, M. (Eds.). (2011). Latinos/as and mathematics education: Research on learning and teaching in classrooms and communities. Charlotte, NC: Information Age Publishing.

    Google Scholar 

  • Thomas, D. (1978). Students’ understanding of selected transformation geometry concepts. In R. Lesh (Ed.), Recent research concerning the development of spatial and geometric concepts (pp. 177–174). Columbus, OH: ERIC.

    Google Scholar 

  • Thomas, N., Mulligan, J., & Goldin, G. (2002). Children’s representation of numbers and structures 1–100. Journal of Mathematical Behavior, 21(1), 117–133. doi:10.1016/S0732-3123(02)00106-2.

    Google Scholar 

  • Thurstone, L., & Thurstone, T. (1941). Factor studies of intelligence. Psychological Monographs, 2.

    Google Scholar 

  • Treacy, K., & Frid, S. (2008). Recognising different starting points in Aboriginal students’ learning of number. In M. Goos, R. Brown, & K. Maker (Eds.), 31st Annual Conference of the Mathematics Education Research Group of Australasia (pp. 531–537). Brisbane: MERGA.

    Google Scholar 

  • Treisman, A. (1988). Features and objects: The fourteenth Bartlett memorial lecture. Quarterly Journal of Experimental Psychology, 40A, 207–237.

    Google Scholar 

  • van der Heijden, A. H. C. (1992). Selective attention in vision. London: Routledge.

    Google Scholar 

  • van Hiele, P. (1986). Structure and insight: A theory of mathematics education. New York: Academic Press.

    Google Scholar 

  • Vandendriessche, E. (2007). Les jeux de ficelle: Une activité mathématique dans certainess sociétés traditionnelles (String figures: A mathematical activity in some traditional societies). Revue d’histoire des mathématiques, 13(1), 7–84.

    Google Scholar 

  • Voigt, J. (1985). Patterns and routines in classroom interaction. Recherches en Didactique des Mathematiques, 6(1), 69–118.

    Google Scholar 

  • Voigt, J. (1994). Negotiation of mathematical meaning and learning mathematics. Educational Studies in Mathematics, 26(2 and 3), 275–298.

    Google Scholar 

  • Vurpillot, E. (1976). The visual world of the child. New York: International Universities Press.

    Google Scholar 

  • Warren, E., Cole, A., & Devries, E. (2009). Closing the gap: Myths and truths behind subitisation. Australasian Journal of Early Childhood, 34(4), 46–53.

    Google Scholar 

  • Webb, N. (1979). Processes, conceptual knowledge and mathematical problem-solving ability. Journal for Research in Mathematics Education, 10, 83–93.

    Google Scholar 

  • Werner, H. (1964). Comparative psychology of mental development (revth ed.). London: International University Press.

    Google Scholar 

  • Wessels, D., & Van Niekerk, R. (1998). Semiotic models and the development of secondary school spatial knowledge. Short oral communication. Paper presented at the 22nd Conference of the International Group for the Psychology of Mathematics PME22, Stellenbosch, South Africa.

    Google Scholar 

  • Wheatley, G., & Cobb, P. (1990). Analysis of young children’s spatial constructions. In L. Steffe & T. Wood (Eds.), Transforming children’s mathematics education (pp. 161–173). Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Wickens, C., & Prevett, T. (1995). Exploring the dimensions of egocentricity in aircraft navigation displays. Journal of Experimental Psychology: Applied, 1(2), 110–135.

    Google Scholar 

  • Willis, S. (2000). Strengthening numeracy: Reducing risk. Paper presented at the ACER Research Conference. Improving Numeracy Learning: What Does the Research Tell Us?, Brisbane, Australia.

    Google Scholar 

  • Wilson, D. (2007). Beyond puzzles: Young children’s shape-composition abilities. In W. G. Martin, M. Strutchens, & P. Elliott (Eds.), The learning of mathematics (NCTM 69th Yearbook) (pp. 239–255). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Witelson, S., & Swallow, J. (1988). Neuropsychological study of the development of spatial cognition. In J. Stiles-Davis, M. Kritchevsky, & U. Bellugi (Eds.), Spatial cognition: Brain bases and development (pp. 373–409). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Wood, T. (2003). Complexity in teaching and children’s mathematical thinking. In N. Pateman, B. Doherty, & J. Zilliox (Eds.), 27th Annual Conference of the International Group for the Psychology in Mathematics Education (Vol. 4, pp. 435–442). Honolulu, Hawaii: PME.

    Google Scholar 

  • Woodward, E., Gibbs, V., & Shoulders, M. (1992). Similarity unit. Arithmetic Teacher, 39(8), 22–25.

    Google Scholar 

  • Zimmermann, W., & Cunningham, S. (Eds.). (1991). Visualisation in teaching and learning mathematics. Washington, DC: Committee on Computers in Mathematics Education of the Mathematical Association of America.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Owens, K. (2015). Visuospatial Reasoning in Twentieth Century Psychology-Based Studies. In: Visuospatial Reasoning. Mathematics Education Library, vol 111. Springer, Cham. https://doi.org/10.1007/978-3-319-02463-9_2

Download citation

Publish with us

Policies and ethics