Designing Digital Technologies and Learning Activities for Different Geometries
 Keith Jones,
 Kate Mackrell,
 Ian Stevenson
 … show all 3 hide
Abstract
This chapter focuses on digital technologies and geometry education, a combination of topics that provides a suitable avenue for analysing closely the issues and challenges involved in designing and utilizing digital technologies for learning mathematics. In revealing these issues and challenges, the chapter examines the design of digital technologies and related forms of learning activities for a range of geometries, including Euclidean and coordinate geometries in two and three dimensions, and nonEuclidean geometries such as spherical, hyperbolic and fractal geometry. This analysis reveals the decisions that designers take when designing for different geometries on the flat computer screen. Such decisions are not only about the geometry but also about the learner in terms of supporting their perceptions of what are the key features of geometry.
Inside
Within this Chapter
 Geometry, Technology, and Teaching and Learning
 Working with Different Geometries on the Flat Screen
 Designing Digital Technologies for Different Geometries
 Designing Learning Activities to Engage Students with Different Geometries
 Shaping, and Being Shaped by, Digital Technologies
 References
 References
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 Abbott, E. A. (1884). Flatland: a romance of many dimensions. London: Seeley.
 Abelson, H., & diSessa, A. (1980). Turtle geometry: the computer as a medium for exploring mathematics. Cambridge, MA: MIT Press.
 Accascina, G., & Rogora, E. (2006). Using 3D diagrams for teaching geometry, International Journal for Technology in Mathematics Education, 13(1), 11–22.
 Arzarello, F., Olivero, F., Paola, D., & Robutti, O. (2002). A cognitive analysis of dragging practices in Cabri environments, ZDM: the International Journal on Mathematics Education, 34(3), 66–72. CrossRef
 Battista, M. T. (2008). Development of the Shape Makers geometry microworld: design principles and research. In G. Blume & M. K. Heid (Eds.) Research on Technology in the Learning and Teaching of Mathematics, Volume 2: Cases and Perspectives (pp. 131–156). Greenwich, CT: Information Age.
 Bessot, A. (1996). Geometry and work: examples from the building industry. In A. Bessott & J. Ridgeway (Eds.) Education for Mathematics in the Workplace (pp. 143–158). Dordrecht: Kluwer.
 Blanchard, P. (1984). Complex analytic dynamics on the Riemann sphere, Bulletin of the American Mathematical Society, 11, 85–141. CrossRef
 Butler, D. (2006). Migrating from 2D to 3D in ‘Autograph’, Mathematics Teaching (Incorporating Micromath), 197, 23–26.
 Christou, C., Jones, K., Mousoulides, N., & Pittalis, M. (2006). Developing the 3DMath dynamic geometry software: theoretical perspectives on design, International Journal of Technology in Mathematics Education, 13(4), 168–174.
 Clements, D. H., Sarama, J., Yelland, N. J., & Glass, B. (2008). Learning and teaching geometry with computers in the elementary and middle school. In M. K. Heid & G. Blume (Eds.) Research on Technology in the Learning and Teaching of Mathematic, Volume 1: Research Syntheses (pp. 109–154). Greenwich, CT: Information Age.
 Garry, T. (1997). Geometer’s sketchpad in the classroom. In J. R. King & D. Schattschneider (Eds.) Geometry Turned On!: Dynamic Software in Learning, Teaching, and Research (pp. 55–62). Washington, DC: The Mathematical Association of America.
 Gawlick, T. (2004). Towards a theory of visualization by dynamic geometry software. Paper presented at the 10th International Congress on Mathematical Education (ICME10), Copenhagen, Denmark, 4–11 July 2004.
 Goldenberg, E. P., & Cuoco, A. (1998). What is dynamic geometry? In R. Lehrer & D. Chazan (Eds.), Designing Learning Environments for Developing Understanding of Geometry and Space. Hilldale, NJ: LEA.
 Goldenberg, E. P., Scher, D., & Feurzeig, N. (2008). What lies behind dynamic interactive geometry software? In G. Blume & M. K. Heid (Eds.) Research on Technology in the Learning and Teaching of Mathematic, Volume 2: Cases and Perspectives (pp. 53–87). Greenwich, CT: Information Age.
 Gray, J. (1989). Ideas of space: Euclidean, nonEuclidean and relativistic. Oxford: Clarendon.
 Harel, I. (Ed.) (1991). Children designers: interdisciplinary constructions for learning and knowing mathematics in a computerrich school. Norwood, NJ: Ablex Publishing.
 Hollebrands, K., Laborde, C., & Strasser, R. (2008). Technology and the learning of geometry at the secondary level. In M. K. Heid & G. Blume (Eds.), Research on Technology in the Learning and Teaching of Mathematic, Volume 1: Research Syntheses (pp. 155–205). Greenwich, CT: Information Age.
 Howson, A. G., & Kahane, J.P. (Eds.) (1986). The influence of computers and informatics on mathematics and its teaching. Cambridge: Cambridge University Press.
 Hoyles, C., Noss, R., & Adamson, R. (2002). Rethinking the microworld idea, Journal of Educational Computing Research, 27(1–2), 29–53. CrossRef
 Jones, K. (1999). Student interpretations of a dynamic geometry environment. In I. Schwank (Ed.), European Research in Mathematics Education (pp. 245–258). Osnabrueck: Forschungsinstitut für Mathematikdidaktik.
 Jones, K. (2009). Linking geometry and algebra in the school mathematics curriculum. In Z. Usiskin (Ed.), Future Curricular Trends in School Algebra and Geometry. Greenwich, CT: Information Age.
 Kaufmann, H., Schmalstieg, D., & Wagner, M. (2000). Construct3D: a virtual reality application for mathematics and geometry education. Education and Information Technologies, 5(4), 263–276. CrossRef
 Kreyzig, E. (1991). Differential geometry. New York: Dover.
 Laborde, C. (1995). Designing tasks for learning geometry in a computerbased environment. In L. Burton & B. Jaworski (Eds.), Technology in Mathematics Teaching: A Bridge Between Teaching and Learning (pp. 35–68). London: ChartwellBratt.
 Laborde, C. (1998). Visual phenomena in the teaching/learning of geometry in a computerbased environment. In C. Mammana & V. Villani (Eds.), Perspectives on the Teaching of Geometry for the 21st Century (pp. 121–128). Dordrecht: Kluwer.
 Laborde, C. (2001). Integration of technology in the design of geometry tasks with CabriGeometry, International Journal of Computers for Mathematical Learning, 6(3), 283–317. CrossRef
 Laborde, C., & Laborde, J.M. (2008). The development of a dynamical geometry environment: Cabrigéomètre. In G. Blume & M. K. Heid (Eds.), Research on Technology in the Learning and Teaching of Mathematic, Volume 2: Cases and Perspectives (pp. 31–52). Greenwich, CT: Information Age.
 Laborde, C., Kynigos, C., Hollebrands, K., & Strasser, R. (2006). Teaching and learning geometry with technology. In A. Gutiérrez & P. Boero (Eds.), Handbook of Research on the Psychology of Mathematics Education: Past, Present and Future (pp. 275–304). Rotterdam: Sense Publishers.
 Mackrell, K. (2008). Cabri 3D: an environment for creative mathematical design. In P. Liljedahl (Ed.), Canadian Mathematics Education Study Group Proceedings 2007 Annual Meeting. Frederickton: University of Frederickton.
 Mandelbrot, B. (1975). Les Objets Fractals: forme, hasard et dimension. Paris: Flammarion.
 Mandelbrot, B. (1980). Fractal aspects of the iteration of z → λ z (1−z) for complex λ and z, Annals of the New York Academy of Sciences, 357, 249–259. CrossRef
 Moustakas, K., Nikolakis, G., Tzovaras, D., & Strintzis, M. G. (2005). A geometry education haptic VR application based on a new virtual hand representation. In Virtual Reality 2005 Proceedings IEEE, Bonn, Germany, March 2005.
 Norman, D. A., & Draper, S. W. (1986). User centered system design: new perspectives on the human–computer interaction. Norwood, NJ: Ablex Publishing.
 Papert, S. (1980). Mindstorms: children, computers, and powerful ideas. New York: Basic Books.
 Papert, S. (1991). In I. Harel & S. Papert (Eds.) Constructionism: research reports and essays 1985–1990. Norwood, NJ: Ablex Publishing.
 Scher, D. (2000). Lifting the curtain: the evolution of the geometer’s sketchpad, The Mathematics Educator, 10(2), 42–48.
 Stevenson, I. (2000). Modelling hyperbolic space: designing a computational context for learning nonEuclidean geometry, International Journal of Computers for Mathematical Learning, 5(2), 143–167. CrossRef
 Stevenson, I., & Noss, R. (1999). Supporting the evolution of mathematical meanings: the case of nonEuclidean geometry, International Journal of Computers for Mathematical Learning, 3(3), 229–254. CrossRef
 Van den Akker, J., Gravemeijer, K., McKenney, S., & Nieveen, N. (Eds.). (2006). Educational design research. London: Routledge.
 Title
 Designing Digital Technologies and Learning Activities for Different Geometries
 Book Title
 Mathematics Education and TechnologyRethinking the Terrain
 Book Subtitle
 The 17th ICMI Study
 Pages
 pp 4760
 Copyright
 2010
 DOI
 10.1007/9781441901460_4
 Print ISBN
 9781441901453
 Online ISBN
 9781441901460
 Series Title
 New ICMI Study Series
 Series Volume
 13
 Series ISSN
 13876872
 Publisher
 Springer US
 Copyright Holder
 SpringerVerlag US
 Additional Links
 Topics
 Keywords

 Design
 Digital technologies
 ICT
 Learning
 Geometry
 Geometries
 eBook Packages
 Editors

 Celia Hoyles ^{(ID1)}
 JeanBaptiste Lagrange ^{(ID2)}
 Editor Affiliations

 ID1. Inst. Education, University College London
 ID2. IUFM de Reims
 Authors

 Keith Jones ^{(1)}
 Kate Mackrell ^{(2)}
 Ian Stevenson ^{(3)}
 Author Affiliations

 1. University of Southampton, Southampton, UK
 2. Queen’s University, Kingston, ON, Canada
 3. King’s College London, London, UK
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