Back to CRME Home PageCollaborative Group for Research in Mathematics Education
Project leader: Constantinos Christou (University of Cyprus)
Team: Keith Jones (University of Southampton, UK), Evgenia Sendova (University of
Sofia, Bulgaria), Joao Filipe Matos (University of Lisbon), Theodosis
Zachariades (University of Athens)
The project is supported by a grant from the EU, award: 224269-CP-1-2005-1-CY-MINERVA-M
Spatial geometry is known to be a difficult subject in every country from nursery school through to university. While three-dimensional (3D) objects are part of our everyday experience, they are usually represented in school geometry lessons by two-dimensional (2D) drawings. Thus learners' understanding of 3D geometry is interrelated with their understanding of 2D geometry. In some cases it can be that there is a conflict between knowledge of plane geometry and an intuition of 3D space. This may be the root of misunderstandings in geometry.
To date, most research concerning spatial ability in 3D geometry deals with solids and their representations (often these representations are in two dimensions). There is much less evidence of learners' understanding of 3D spatial relationships not in the context of solids, for example geometric concepts such as lines and plane and the relationships between them such as parallelism and perpendicularity.
The aim of this project to devise and test a teaching programme in 3D geometry for middle school students based on the needs, knowledge and experiences of a range of countries within the European Union. The main objective of the project is the development (and testing) of a dynamic three-dimensional geometry microworld, which enables students to construct, observe and manipulate geometrical figures in space, and which teachers can use to help students construct understanding of stereometry.
Full details of the project are on the main project website.
Publications (in date order)
Christou, C., Jones, K.,
Pitta-Pantazi, D., Pittalis, M., Mousoulides, N., Matos, J. F., Sendova, E.,
Zachariades, T. and Boytchev, P. (2007), Developing student spatial ability with
3D software applications. Paper presented at the 5th Congress of the European
Society for Research in Mathematics Education (CERME5), Larnaca, Cyprus,
22-26 Feb 2007. 10pp.
Click here for
full article in pdf format.
Christou, C., Pittalis, M., Mousoulides, N., Pitta, D., Jones, K., Sendova,
E. and Boytchev, P. (2007) Developing an active learning environment for the
learning of stereometry. Paper presented at the 8th International Conference
on Technology and Mathematics Teaching (ICTMT8), Hradec Králové, Czech
Republic, 1-4 Jul 2007. 5pp.
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full article in pdf format.
Christou, C., Jones, K., Mousoulides, N. and Pittalis, M. (2006),
Developing the 3DMath dynamic geometry software:
theoretical perspectives on design, International Journal for Technology in Mathematics Education,
13(4), 168-174.
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full article in pdf format.
Christou, C., Pittalis, M., Mousoulides, N., & Jones, K. (2005), Developing
3D Dynamic Geometry Software: theoretical perspectives on design. In F. Olivero
& R. Sutherland (Eds), Visions of Mathematics Education: Embedding Technology
in Learning; Proceedings of the 7th International Conference on Technology and
Mathematics Teaching. Bristol, UK, 26-29 July 2005. Vol 1 pp 69-77. ISBN:
0862925592
Click here for
full article in pdf format.
Conference Presentations
5th Congress of the European Society for Research in Mathematics Education (CERME5), Larnaca, Cyprus, February 2007.
7th International Conference on Technology and Mathematics Teaching. Bristol, UK, 2005.
Related CRME Projects
CalGeo: teaching calculus using dynamic geometric tools
The project is supported by a grant from the EU, award:
11892-CP-1-2004-1-GR-COMENIUS-C21
The
Mediation of Learning in Dynamic Geometry Environments
This research was part-supported by grant A94/16 from
the University of Southampton Research Fund.
Manipulatives in Teacher
Education in Geometry
This project was supported by a from the Brazilian
Ministry of Education Conselho Nacional de Desenvolvimento
Científico e Tecnológico (CNPq), grant number 201535/93.
Indicative bibliography
Alsina, C. (2001), Gaudi's Ideas For Your Classroom: Geometry For Three-Dimensional Citizens. Selected Lectures ICME-9, Makuhari-Tokyo (Japan), 1-8.
Cohen, N. (2000), Misconceptions in 3-D Geometry Basic Concepts, Proceedings of the 24th Conference of the International Group for the Psychological of Mathematics Education, Hiroshima, Japan, Vol.1, p.149.
Cohen, N. (2003), Preference of Directions in 3D Space. Proceedings of CERME3, Italy, 2002.
Gutiérrez, A. (1992), Exploring the links between Van Hiele Levels and 3-dimensional geometry, Structural Topology, 18, 31-48.
Gutiérrez, A. & Jaime, A. (1993), An analysis of the students' use of mental images when making or imagining movements of polyhedra, Proceedings of the 17th PME Conference, Vol 2, pp. 153-160.
Gutiérrez, A. (1996), Visualization in 3-dimensional Geometry: in search of a framework, Proceedings of the 20th Psychology of Mathematics Education Conference, Vol 1, pp. 3-19.
Page updated 26 March 2008
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