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Spatial Abilities Research as a Foundation for Visualization in Teaching and Learning Mathematics

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Critical Issues in Mathematics Education

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References

  • Anderson, M., Sáenz-Ludlow, A., Zellweger, Z., & Cifarelli, V. V. (Eds.). (2003). Educational perspectives on mathematics as semiosis: From thinking to interpreting to knowing. New York: Legas.

    Google Scholar 

  • Aspinwall, L., Shaw. K. L., & Presmeg, N. C. (1997). Uncontrollable mental imagery: Graphical connections between a function and its derivative. {\it Educational Studies in Mathematics, 33(3), 301–317.

    Article  Google Scholar 

  • Bishop, A. J. (1980). Spatial abilities and mathematics education – a review. Educational Studies in Mathematics, 11, 257–269.

    Article  Google Scholar 

  • Bishop, A. J. (1983). Space and geometry. In R. Lesh & M. Landau (Eds.), Acquistion of mathematical concepts and processes (pp. 175–203). New York: Academic Press.

    Google Scholar 

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

    Google Scholar 

  • Bishop, A. J. (1988b). Mathematics education in its cultural context. Educational Studies in Mathematics, 19, 179–191. [Reprinted 2004 as Chapter 16 in T. P. Carpenter, J. A. Dossey, and J. L. Koehler (Eds.), Classics in mathematics education research (pp. 201–207). Reston, Virginia: National Council of Teachers on Mathematics.]

    Article  Google Scholar 

  • Bishop, A. J., (1989). Review of research on visualization in mathematics education. {\it Focus on Learning Problems in Mathematics, 11(1), 7–16.

    Google Scholar 

  • Bishop, A. J., Clements, K., Keitel, C., Kilpatrick, J., & Laborde, C. (Eds.). (1996). International handbook of mathematics education. Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Clements, M. A. (1978). Some mathematics educators’ view on spatial ability. In B. Low, M. E. Dunkley, & J. Conroy (Eds.), Research in mathematics education in Australia, 1978. Sydney, Australia: Macquarrie University.

    Google Scholar 

  • Cobb, P. (2007). Putting philosophy to work. In F. K. Lester, Jr. (Ed.), Second handbook of research in mathematics teaching and learning (pp. 3–38). Charlotte, NC: Information Age Publishing.

    Google Scholar 

  • Denzin, N. K., & Lincoln, Y. S. (Eds.). (2000). Handbook of qualitative research. Thousand Oaks, California: Sage Publications.

    Google Scholar 

  • English, L. D. (Ed.) (2002). Handbook of international research in mathematics education. Mahwah, New Jersey: Lawrence Erlbaum Associates.

    Google Scholar 

  • Goldin, G. A., & Janvier, C. (Eds.). (1998). Representations and the psychology of mathematics education. Special double issue of The Journal of Mathematical Behavior, 11 & 12.

    Google Scholar 

  • Gravemeijer, K., Lehrer, R., van Oers, B., & Verschaffel, L. (Eds.). (2002). Symbolizing, modeling and tool use in mathematics education. Dordrecht, The Netherlands: Kluwer Academic Publishers.

    Google Scholar 

  • Gray, E. (1999). Spatial strategies and visualization. In O. Zaslavsky (Ed.), Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education, 1, 235–242.

    Google Scholar 

  • Grouws, D. A. (Ed.) (1992). Handbook of research on mathematics teaching and learning. New York: Macmillan.

    Google Scholar 

  • Gutierrez, A., Jaime, A., & Fortuny, J. M. (1991). As alternative paradigm to evaluate the acquisition of the van Hiele levels. {\it Journal for Research in Mathematics Education, 22(3), 231–251.

    Google Scholar 

  • Hitt, F. (Ed.). (2002). Representations and mathematics visualization. Mexico City: Cinvestav-IPN.

    Google Scholar 

  • Hostetler, K. (2005). What is “good” educational research? {\it Educational Researcher, 34(6), 16–21.

    Article  Google Scholar 

  • Johnson, R. K., & Onwuegbuzie, A. J. (2004). Mixed methods research: A research paradigm whose time has come. {\it Educational Researcher, 33(7), 14–26.

    Article  Google Scholar 

  • Kelly, A. E., & Lesh, R. A. (Eds.). (2000). Handbook or research design in mathematics and science education. Mahwah, New Jersey: Lawrence Erlbaum Associates.

    Google Scholar 

  • Kirshner, D., & Whitson, J. A. (Eds.). (1997). Situated cognition: Social, semiotic, and psychological perspectives. Mahwah, New Jersey: Lawrence Erlbaum Associates.

    Google Scholar 

  • Krutetskii, V. A. (1969). Papers in J. Kilpatrick & I. Wirszup (Eds.), Soviet studies in mathematics education: Vol. II, The structure of mathematical abilities. Chicago: University of Chicago Press.

    Google Scholar 

  • Krutetskii, V. A. (1976). The psychology of mathematical abilities in school children. Edited by J. Kilpatrick & I. Wirszup. Chicago: University of Chicago Press.

    Google Scholar 

  • Lave, J. (1997). The culture of acquisition and the practice of understanding. In D. Kirshner & J. A. Whitson (Eds.), Situated cognition: Social, semiotic, and psychological perspectives (pp. 17–35). Mahwah, New Jersey: Lawrence Erlbaum Associates.

    Google Scholar 

  • Lean, G. A. (1981). Spatial training studies and mathematics education: A review. Unpublished paper, University of Cambridge.

    Google Scholar 

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

    Article  Google Scholar 

  • Lehrer, R., & Pritchard, C. (2002). Symbolizing space into being. In K. Gravemeijer, R. Lehrer, B. van Oers, & L. Verschaffel (Eds.), Symbolizing, modeling and tool use in mathematics education (pp. 59–86). Dordrecht, The Netherlands: Kluwer Academic Publishers.

    Google Scholar 

  • Lester, F. K., Jr. (Ed.). (2007). Second handbook of research in mathematics teaching and learning. Charlotte, NC: Information Age Publishing.

    Google Scholar 

  • Mariotti, M. A. (2002). Influences of technologies’ advances on students’ mathematics learning. In L. D. English (Ed.), Handbook of international research in mathematics education (pp. 695–723). Mahwah, New Jersey: Lawrence Erlbaum Associates.

    Google Scholar 

  • National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, Virginia: The Council.

    Google Scholar 

  • Neisser, U. (1970). Visual image as process and as experience. In J. S. Antrobus (Ed.), Cognition and effect. Boston: Little & Brown.

    Google Scholar 

  • Owens, K. (1999). The role of visualisation in young students’ learning. In O. Zaslavsky (Ed.), Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education, 1, pp. 220–234.

    Google Scholar 

  • Parzysz, B. (1999). Visualization and modeling in problem solving: From algebra to geometry and back. In O. Zaslavsky (Ed.), Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education, 1, pp. 212–219.

    Google Scholar 

  • Peirce, C. S. (1992). The essential Peirce (vol. 1) Edited by N. Houser & C. Kloesel. Bloomington: Indiana University Press.

    Google Scholar 

  • Peirce, C. S. (1998). The essential Peirce (vol. 2) Edited by the Peirce Edition Project. Bloomington: Indiana University Press.

    Google Scholar 

  • Presmeg, N. C. (1985). The role of visually mediated processes in high school mathematics: A classroom investigation. Unpublished Ph.D. dissertation, University of Cambridge.

    Google Scholar 

  • Presmeg, N. C. (1992). Prototypes, metaphors, metonymies, and imaginative rationality in high school mathematics. Educational Studies in Mathematics, 23, 595–610.

    Article  Google Scholar 

  • Presmeg, N. C. (1997). Generalization using imagery in mathematics. In L. D. English (Ed.), Mathematical reasoning: Analogies, metaphors and images (pp. 299–312). Mahwah, New Jersey: Lawrence Erlbaum Associates.

    Google Scholar 

  • Presmeg, N. C. (2006a). Research on visualization in learning and teaching mathematics. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 205–235). Rotterdam, The Netherlands: Sense Publishers.

    Google Scholar 

  • Presmeg, N. C. (2006b). A semiotic view of the role of imagery and inscriptions in mathematics teaching and learning. Plenary Paper. In J. Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceedings of the 30th Annual Meeting of the International Group for the Psychology of Mathematics Education, 1, 19–34. Prague, July 16–21, 2006.

    Google Scholar 

  • Richardson, A. (1969). Mental imagery. London: Routledge & Kegan Paul.

    Google Scholar 

  • Richardson, A. (1972). Voluntary control of the memory image. In P. W. Sheehan (Ed.), The function and nature of imagery. New York: Academic Press.

    Google Scholar 

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

    Article  Google Scholar 

  • Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In Kelly, A. E. & Lesh, R. A. (Eds.), Handbook or research design in mathematics and science education (pp. 267–306). Mahwah, New Jersey: Lawrence Erlbaum Associates.

    Google Scholar 

  • Wheatley, G. H. (1997). Reasoning with images in mathematical activity. In L. D. English (Ed.), Mathematical reasoning: Analogies, metaphors and images (pp. 281–297). Mahwah, New Jersey: Lawrence Erlbaum Associates.

    Google Scholar 

  • Yerushalmy, M., Shternberg, B., & Gilead, S. (1999). Visualization as a vehicle for meaningful problem solving in algebra. In O. Zaslavsky (Ed.), Proceedings of the 23rd conference of the international group for the psychology of mathematics education, 1, pp. 197–211.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Illinois State University, 313 Stevenson Hall, Normal IL 61790-4520, USA

    Norma Presmeg

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  1. Norma Presmeg
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Editor information

Editors and Affiliations

  1. Faculty of Education, Australian Catholic University, Fitzroy VIC 3065, Australia

    Philip Clarkson

  2. Department of Mathematics, Illinois State University, 313 Stevenson Hall, Normal IL 61790-4520, USA

    Norma Presmeg

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Presmeg, N. (2008). Spatial Abilities Research as a Foundation for Visualization in Teaching and Learning Mathematics. In: Clarkson, P., Presmeg, N. (eds) Critical Issues in Mathematics Education. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-09673-5_6

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