Skip to main content
SpringerLink
Log in

Introduction: Visuospatial Reasoning in Context

  • Chapter
  • First Online:
Visuospatial Reasoning

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

Abstract

An historical overview is presented of relevant research on spatial abilities and visual imagery but the issues related to visuospatial reasoning highlighted by national school test performance show the dilemma mathematics education faces. The importance of visuospatial reasoning is illustrated by examples and by reference to important fields such as geography, science, and mathematics. A preliminary definition is provided which covers a wide range of mental activities and physical representations under the umbrella of visuospatial reasoning. Its importance for geometry learning is established before arguing the need to extend our understanding of visuospatial reasoning by looking at critical place-based education and Indigenous cultures. Subsequently, a diagrammatic summary is presented to show how ecocultural contexts influence ecocultural identity and the self-regulated learner whose reasoning (including visuospatial reasoning), goals, and self-evaluations surrounded by affective characteristics impact on responsiveness resulting in an ecocultural mathematical identity. This chapter acts as an introductory overview for the book and presents the challenges that are addressed in each chapter before moving on to Chap. 2.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
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

Similar content being viewed by others

References

  • Adler, J. (2002). Teaching mathematics in multilingual classrooms. New York: Kluwer.

    Google Scholar 

  • Atweh, B., Barton, A. C., & Borba, M. (Eds.). (2007). Internationalisation and globalisation in mathematics and science education. Dotrecht, The Netherlands: Springer.

    Google Scholar 

  • Australian Council for Educational Research. (1989–1991). Aspects of numeracy. Basic skills tests for years 3 and 6. Sydney: NSW Department of School Education.

    Google Scholar 

  • Barnhardt, R. (2007). Creating a place for Indigneous knowledge in education: The Alaska Native Knowledge Network. In D. Gruenewald & G. Smith (Eds.), Place-based education in the global age: Local diversity (pp. 113–133). New York: Lawrence Erlbaum.

    Google Scholar 

  • Barton, B. (2008). The language of mathematics: Telling mathematical tales. New York: Springer.

    Book  Google Scholar 

  • Battista, M. (2007a). The development of geometric and spatial thinking. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 843–903). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

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

    Book  Google Scholar 

  • Brofenbrenner, U., & Ceci, S. (1994). Nature-nurture reconceptualized in developmental perspective: A bioecological model. Psychological Review, 101(4), 568–586.

    Article  Google Scholar 

  • Brown, A., & Clark, L. (Eds.). (2006). Learning from NAEP: Professional development materials for teachers of mathematics (with CD). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Campbell, K., Collis, K., & Watson, J. (1995). Visual processing during mathematical problem solving. Educational Studies in Mathematics, 28(2), 177–194.

    Article  Google Scholar 

  • Casey, B., Dearing, E., Vasilyeva, M., Ganley, C., & Tine, M. (2011). Spatial and numerical predictors of measurement performance: The moderating effects of community income and gender. Journal of Educational Psychology, 103(2), 296–311.

    Article  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 

  • Clarkson, P., & Presmeg, N. (Eds.). (2008). Critical issues in mathematics education: Major contributions of Alan Bishop. New York: Springer.

    Google Scholar 

  • Clements, M., Bishop, A., Keitel, C., Kilpatrick, J., & Leung, F. (Eds.). (2013). Third international handbook of mathematics education. New York: Springer.

    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 

  • Costigan, K. (1995). The patterns of structure in the Trobriand Islands. M.S. Architecture Master of Science, University of California, Berkeley, CA.

    Google Scholar 

  • Davis, B. (1999). Thinking otherwise and hearing differently: Enactivism and school mathematics. In W. F. Pinar (Ed.), Contemporary curriculum discourses: Twenty years of JCT (pp. 325–345). New York: Lang.

    Google Scholar 

  • Diezmann, C., & Lowrie, T. (2012). Learning to think spatially: What do students “see” in numeracy test items? International Journal of Science and Mathematics Education, 10(6), 1469–1490. doi:10.1007/s10763-012-9350-3.

    Article  Google Scholar 

  • Eglash, R. (2007). Culturally situated design tools: Teaching math through culture. Retrieved from http://www.rpi.edu/~eglash/csdt.html

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

    Book  Google Scholar 

  • Ellerton, N., & Clements, M. (1994). The national curriculum debacle. Perth, WA, Australia: Meridian Press.

    Google Scholar 

  • Falcade, R., Laborde, C., & Mariotti, M. (2007). Approaching functions: Cabri tools as instruments of semiotic mediation. Educational Studies in Mathematics, 66(3), 317–333.

    Article  Google Scholar 

  • Ferrare, J., & Apple, M. (2012). Spatializing critical education: Progress and cautions. Critical Studies in Education, 51(2), 209–221. doi:http://dx.doi.org/10.1080/17508481003731075.

    Article  Google Scholar 

  • Gervasoni, A. (2005). Australian Catholic University—Pursuing its mission to engage with communities: A case study of the Melbourne and Ballarat campuses (A research report for the Australian Consortium of Higher Education ). Melbourne: Australian Catholic University.

    Google Scholar 

  • Goldenberg, P., Cuoco, A., & Mark, J. (1998). A role for geometry in general education. In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 3–44). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Goldin, G. (2000). Affective pathways and representation in mathematical problem solving. Mathematical Thinking and Learning: An International Journal, 2(3), 209–219.

    Article  Google Scholar 

  • Gruenewald, D. (2008). The best of both worlds: A critical pedagogy of place. Environmental Education Research, 14(3), 308–324.

    Google Scholar 

  • Gruenewald, D., & Smith, G. (2007). Place-based education in a global age: Local diversity. New York: Lawrence Erlbaum.

    Google Scholar 

  • Gutiérrez, A. (1996). Visualization in 3-dimensional geometry: In search of a framework. In L. Puig & A. Gutiérrez (Eds.), 20th Conference of the International Group for Psychology of Mathematics Education (Vol. 1, pp. 3–17). Valencia, Portugal: University of Valencia.

    Google Scholar 

  • Gutiérrez, A., & Boero, P. (Eds.). (2006). Handbook of research on the psychology of mathematics education: Past, present and future: PME 1976-2006. Rotterdam, The Netherlands: Sense Publishers.

    Google Scholar 

  • Hutchins, E. (1983). Understanding Micronesian navigation. In D. Gentner & A. Stevens (Eds.), Mental models (pp. 191–225). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Johnston-Wilder, S., & Mason, J. E. (2005). Developing thinking in geometry. London: Open University and Paul Chapman.

    Google Scholar 

  • Jonassen, D., Peck, K., & Wilson, B. (1999). Learning with technology: A constructivist perspective. Upper Saddle River, NJ: Prentice Hall.

    Google Scholar 

  • Jones, J. (2012). Visualizing elementary and middle school mathematics methods. Hoboken, NJ: Wiley.

    Google Scholar 

  • Kahan, S. (2004). Engagement, identity and innovation: Etienne Wenger on communities of practice. Journal of Association Leadership. Retrieved from http://www.asaecenter.org/PublicationsResources/JALArticleDetail.cfm?ItemNumber=16217

  • Kilpatrick, J., Martin, W., & Schifter, D. (Eds.). (2003). A research companion to Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics.

    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.

    Article  Google Scholar 

  • Kimball, S. T. (1974). Culture and the educative process. New York: Teachers College Press.

    Google Scholar 

  • Kouba, V., Brown, C., Carpenter, T., Lindquist, M., Silver, E., & Swafford, J. (1988). Results of the fourth NAEP assessment of mathematics: Measurement, geometry, data interpretation, attitudes, and other topics. Arithmetic Teacher, 35(9), 10–16.

    Google Scholar 

  • Lappan, G. (1999, December). Geometry: The forgotten strand. National Council of Teachers of Mathematics News Bulletin.

    Google Scholar 

  • Lave, J. (1988). Cognition in practice. Cambridge, MA: Harvard University Press.

    Book  Google Scholar 

  • Lester, F. (Ed.). (2007). Second handbook of research on mathematics teaching and learning. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Liben, L. S. (1988). Conceptual issue in the development of spatial cognition. In J. Stiles-Davis, M. Kritchevsky, & U. Bellugi (Eds.), Spatial cognition: Brain bases and development (pp. 167–194). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

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

    Article  Google Scholar 

  • Llewellyn, G. (1991). The teenage liberation handbook: How to quit school and get a real life and education. Eugene, OR: Lowry House Publishers.

    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 

  • Lovat, T., & Toomey, R. (Eds.). (2009). Values education and quality teaching: Double helix effect. Dordrecht, The Netherlands: Springer.

    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 

  • Macmillan, A. (2009). Numeracy in early childhood. Sydney, NSW: Oxford University Press.

    Google Scholar 

  • Mammana, C., & Villani, V. (Eds.). (1998). Perspectives on the teaching of geometry for the 21st century. New York: Springer.

    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 

  • Matang, R. (1998). The role of ethnomathematics and reflective learning in mathematics education in Papua New Guinea. Directions: Journal of Educational Studies, 20(2), 22–29.

    Google Scholar 

  • Molnar, J., & Slezakova, J. (2012). Testing of geometrical imagination—Poster 16. 12th International Congress on Mathematics Education ICME12 (pp. 7516). Seoul, Korea: ICME12.

    Google Scholar 

  • Muke, C. (2000). Ethnomathematics: Mid-Wahgi counting practices in Papua New Guinea. Masters thesis, University of Waikato, Waikato, New Zealand.

    Google Scholar 

  • Mullis, I. V. S., Martin, M. O., Kennedy, A. M., & Foy, P. (2007). PIRLS 2006 International Report. IEA’s progress in international reading literacy study in primary school in 40 countries. Chestnut Hill, MA: TIMSS and PIRLS International Study Center, Boston College.

    Google Scholar 

  • Munn, N. (1961). Psychology: The fundamentals of human adjustment (4th ed.). Boston: Houghton Mifflin.

    Google Scholar 

  • National Research Council Committee on Geography. (2006). Learning to think spatially: GIS as a support system in the K-12 curriculum. Washington, DC: National Academies Press.

    Google Scholar 

  • Ness, D., & Farenga, S. (2007). Knowledge under construction: The importance of play in developing children’s spatial and geometric thinking. Lanham, Maryland: Rowan & Littlefield.

    Google Scholar 

  • Nunes, T. (1992). Ethnomathematics and everyday cognition. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 557–574). New York: Macmillan.

    Google Scholar 

  • O’Sullivan, D. (2008). The Treaty of Waitangi in contemporary New Zealand politics. Australian Journal of Political Science, 43(2), 317–331.

    Article  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. (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. (1999b). The role of culture and mathematics in a creative design activity in Papua New Guinea. In E. Ogena & E. Golla (Eds.), 8th South-East Asia Conference on Mathematics Education: Technical papers (pp. 289–302). Manila, The Philippines: Southeast Asian Mathematical Society.

    Google Scholar 

  • Owens, K. (2008). Diversity of approaches to mathematics education in a cultural context. Proceedings of the Conference of the International Study Group on the Relations Between History and Pedagogy of Mathematics, HPM2008. Mexico City: Organising Committee HPM2008.

    Google Scholar 

  • Owens, K. (2012a). Identity and ethnomathematics projects in Papua New Guinea. In D. Jaguthsing, L. P. Cheng, & S. F. Ng (Eds.), Mathematics Education: Expanding Horizons. Proceedings of 35th Annual Conference of Mathematics Education Research Group of Australasia. Singapore: MERGA.

    Google Scholar 

  • Owens, K. (2014). The impact of a teacher education culture-based project on identity as a mathematics learner. Asia-Pacific Journal of Teacher Education, 42(2), 186–207. doi:10.1080/1359866X.2014.892568.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Owens, K., Doolan, P., Bennet, M., Logan, P., Murray, L., McNair, M., et al. (2012). Continuities in education: Pedagogical perspectives and the role of Elders in education for Indigenous students. Journal of Australian Indigenous Issues, 15(1), 20–39.

    Google Scholar 

  • Owens, K., McPhail, D., & Reddacliff, C. (2003). Facilitating the teaching of space mathematics: An evaluation. In N. Pateman, B. Dougherty, & J. Zilliox (Eds.), Proceedings of 27th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 339–345). Hawaii: International Group for the Psychology of Mathematics Education.

    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 

  • Pegg, J., & Davey, G. (1998). Interpreting student understanding in geometry: A synthesis of two models. In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 109–136). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Perry, B., Anthony, G., & Diezmann, C. (Eds.). (2004). Research in mathematics education in Australasia 2000–2003. Sydney: MERGA.

    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 

  • 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 

  • 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 and 3), 165–190.

    Google Scholar 

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

    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 

  • Rosa, M., & Orey, D. (2012). Ethnomodeling: A pedagogical action for uncovering ethnomathematical practices. International Congress on Mathematics Education. Retrieved from http://www.icme12.org/upload/UpFile2/TSG/1799.pdf

  • Royal Society, & Joint Mathematical Council. (2001). Teaching and learning geometry Pre-19. London: Author.

    Google Scholar 

  • Saxe, G., & Esmonde, I. (2005). Studying cognition in flux: A historical treatment of fu in the shifting structure of Oksapmin mathematics. Mind, culture, and activity, 12(3), 171–225.

    Article  Google Scholar 

  • Senechal, M. (1991). Visualisation and visual thinking. In J. Malkevitch (Ed.), Geometry’s future (pp. 15–21). Arlington, MA: Community Map Analysis Project.

    Google Scholar 

  • Shah, P., & Miyake, A. (2005). The Cambridge handbook of visuospatial thinking. New York: Cambridge University Press.

    Book  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 

  • Stigler, J., & Baranes, R. (1988). Culture and mathematics learning. Review of Research in Education, 15, 253–306.

    Google Scholar 

  • Sturrock, F., & May, S. (2002). Programme for International Student Assessment (PISA 2000): The New Zealand Context. The reading, mathematical and scientific literacy of 15-year-olds. Wellington, NZ: Ministry of Education.

    Google Scholar 

  • Thornton, M., & Watson-Verran, H. (1996). Living maths. Abbotsford, Victoria: Yirrkala Community School and Boulder Valley Films.

    Google Scholar 

  • Tuan, Y.-F. (1977). Space and place: The perspective of experience. London: Edward Arnold.

    Google Scholar 

  • Valero, P., & Zevenbergen, R. (Eds.). (2004). Researching the socio-political dimensions of mathematics education: Issues of power in theory and methodology. New York: Kluwer.

    Google Scholar 

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

    Google Scholar 

  • Walkerdine, V. (1988). The mastery of reason. Cambridge: Routledge.

    Google Scholar 

  • Watson, R. (1965). Psychology of the child (2nd ed.). New York: Wiley.

    Google Scholar 

  • Wenger, E. (1998). Communities of practice: Learning, meaning, and identity. New York: Cambridge University Press.

    Book  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 

  • Worsley, P. (1997). Knowledges: Culture, counterculture, subculture. New York: The New Press.

    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

  1. School of Teacher Education, Charles Sturt University, Dubbo, NSW, Australia

    Kay Owens

Authors
  1. Kay Owens
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Owens, K. (2015). Introduction: Visuospatial Reasoning in Context. In: Visuospatial Reasoning. Mathematics Education Library, vol 111. Springer, Cham. https://doi.org/10.1007/978-3-319-02463-9_1

Download citation

Publish with us

Policies and ethics

Search

Navigation