Back to CRME Home PageCollaborative Group for Research in Mathematics Education
Project team: Keith Jones; Liping Ding;
Principal collaborator: Taro Fujita (University of Plymouth)
International Collaborators: Susumu Kunimune (Shizuoka
University, Japan), Shinya Yamamoto (Kumamoto University, Japan)
The project is supported by a University of Southampton School of Education Scholarship and ORS award 2005037007.
This focus for this project is analysing the approaches to the teaching of geometrical ideas in secondary mathematics and is currently examining teaching approaches in China, Japan and the UK.
School geometry is commonly regarded as a key topic in which to develop students' deductive reasoning and creative thinking. Yet while deductive reasoning is central to making progress in mathematics, it remains the case that pupils at the secondary school level have great difficulty in making the transition to this form of reasoning. This study focuses on analysing the teaching approaches employed in different socio-cultural contexts, China, England and Japan, selected because they have long established, but contrasting, pedagogic traditions. The study aims to make a significant contribution to the development of pedagogic theory in the area of the teaching of geometry. The intention is to test and, where appropriate, develop, the van Hiele model of geometry learning through analysing current geometry curricula at the secondary school level in the selected countries. Teaching approaches to geometry are being examined through sampling teaching material, questionnaires to teachers, and classroom observation. The outcomes are intended to inform the development of school geometry curricula to take account of new teaching methods and new technology.
Publications (in date order)
Ding, L. and Jones, K. (2007), Using the van Hiele theory to analyse the
teaching of geometrical proof at Grade 8 in Shanghai, China. In D.
Pitta-Pantazi & G. Philippou (Eds), European Research in Mathematics
Education V (pp 612-621). Nicosia, Cyprus: University of Cyprus. ISBN:
9789963671250
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full article in pdf format.
Ding, L. & Jones, K. (2006), Students' Geometrical Thinking Development at
Grade 8 in Shanghai, In Novotná, J., Moraová, H., Krátká, M. & Stehlíková, N.
(Eds.), Proceedings 30th Conference of the International Group for the
Psychology of Mathematics Education (PME30), vol 1, p382. [extended
abstract]
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full article in pdf format.
Jones, K., Fujita, T. & Ding, L. (2006), Informing the pedagogy for geometry:
learning from teaching approaches in China and Japan, Proceedings of the
British Society for Research into Learning Mathematics, 26(2),
109-114.
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full article in pdf format.
Ding, L. & Jones, K. (2006), Teaching geometry in lower secondary school in
Shanghai, China, Proceedings of the British Society for Research into
Learning Mathematics, 26(1), 41-46.
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full paper in pdf format.
Jones, K., Fujita, T. and Ding, L. (2005), Developing Geometrical Reasoning
in the Classroom: learning from expert teachers from China and Japan, Paper
presented at the 4th Biennial Conference of the European Society for Research
in Mathematics Education (CERME4), Spain, February 2005.
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full paper in pdf format
Also presented as: Jones, K., Fujita, T. and Ding, L. (2005), Teaching
Geometrical Reasoning: learning from expert teachers from China and Japan, Paper
presented at the 6th British Congress on Mathematical Education (BCME6),
Warwick, March 2005. Available as: Jones, K., Fujita, T. and Ding, L. (2005),
Teaching Geometrical Reasoning: learning from expert teachers from China and
Japan, Proceedings of the British Society for Research into Learning
Mathematics, 25(1), 89-96.
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full paper in pdf format
Ding, L. and Jones, K. (2004), The structure of mathematics lessons: researching the development of geometrical reasoning in lower secondary schools in China. Paper presented at the European Society for Research in Mathematics Education Summer School, Podebrady, Czech Republic, August 2004
Fujita, T. and Jones, K. (2003), Interpretations of National Curricula:
the case of geometry in Japan and the UK. Paper presented at the British
Educational Research Association Annual Conference, Heriot-Watt University,
10-13 September, 2003.
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full article in pdf format.
Fujita, T. and Jones, K. (2003), Critical Review of Geometry in Current
Textbooks in Lower Secondary Schools in Japan and the UK, Proceedings of the
27th Conference of the International Group for the Psychology of Mathematics
Education, Vol 1, 220 [extended abstract].
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the extended abstract in pdf format.
Fujita, T. and Jones, K. (2002), Opportunities for the Development of
Geometrical Reasoning in Current Textbooks in the UK and Japan, Proceedings
of the British Society for Research into Learning Mathematics, 22(3),
79-84.
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full paper in pdf format.
Conference Presentations
5th Congress of the European Society for Research in Mathematics Education (CERME5), Larnaca, Cyprus, February 2007.
European Society for Research in Mathematics Education Summer School, Finland, August 2006
30th Conference of the International Group for the Psychology of Mathematics Education (PME30), Prague, 2006.
Conference of the British Society for Research into Learning Mathematics, June 2006
Conference of the British Society for Research into Learning Mathematics, February 2006
6th British Congress on Mathematical Education (BCME6), Warwick, March 2005
4th Biennial Conference of the European Society for Research in Mathematics Education (CERME4), Spain, February 2005.
British Educational Research Association Annual Conference (BERA2004), University of Manchester, 15-18 September 2004
European Society for Research in Mathematics Education Summer School, Podebrady, Czech Republic, August 2004
British Educational Research Association Annual Conference (BERA2004), Heriot-Watt University, 10-13 September, 2003.
Related CRME Projects
Developments
in the Geometry Curriculum in the UK and Japan
This project was supported by a full-time research
student with funding from Japan.
Annotated Bibliography of Chinese Research in Mathematics Education
For an annotated bibliography of Chinese Research in Mathematics Education, click here.
Selected bibliography of research relevant to a comparative study of geometry education
Clarke, D. (2003), The Structure of Mathematics Lessons in Australia. Paper presented as part of the symposium "Mathematics Lessons in Germany, Japan, the USA and Australia: Structure in Diversity and Diversity in Structure" at the Annual Meeting of the American Educational Research Association, Chicago, April 21-25, 2003.
Duval, R. (1998) Geometry from a cognitive point of view. In: C. Mammana and V. Villani (eds.) Perspectives on the Teaching of Geometry for the 21st Century, An ICMI Study [Chapter 2.2]. The Netherlands: Kluwer Academic Publishers.
Hansen, V. L. (1998) Everlasting geometry. In: C. Mammana and V. Villani (eds.) Perspectives on the Teaching of Geometry for the 21st Century, An ICMI Study [Chapter 1.1]. The Netherlands: Kluwer Academic Publishers.
Hershkowitz, R. (1990) Psychological aspects of Learning Geometry. In: P. Nesher and J. Kilpatrick (Eds.), Mathematics and Cognition. (pp. 70-95). Cambridge, Cambridge University Press.
Hershkowitz, R. (1998) About reasoning in geometry. In: C. Mammana and V. Villani (eds.) Perspectives on the Teaching of Geometry for the 21st Century, An ICMI Study [Chapter 2.1]. The Netherlands: Kluwer Academic Publishers.
Hiebert, J., Gallimore, R., Garnier, H., Giwin, K.B., Hollingsworth, H., Jacobs, J., Chui, M.Y., Wearne, D., Smith, M, Kersting, N., Manaster, A., Tseng, E., Etterbeek, W., Manaster, C., Gonzales, P. and Stigler, J. (2003) Teaching Mathematics in Seven Countries: Results from the TIMSS 1999 video study. Washington: NCES, U.S. Department of Education, Institute of Education Sciences.
Hoyles, C., Foxman, D. and Küchemann, D.: 2002, A Comparative Study of Geometry Curricula. London: Qualifications and Curriculum Authority.
Jones, K. (2002), Issues in the teaching and learning of geometry. In,
Haggarty, L. (ed.) Aspects of teaching secondary mathematics: perspectives on
practice. London, UK, Routledge Falmer, 121-139. ISBN: 0-415-26641-6
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full article in pdf format.
Mammana, C. and Villani, V. (eds.) (1998) Perspectives on the Teaching of Geometry for the 21st Century, An ICMI Study. The Netherlands: Kluwer Academic Publishers.
Royal Society and Joint Mathematical Council: 2001, Teaching and Learning Geometry 11-19, London, Royal Society/Joint Mathematical Council.
Schmidt, W. H. et al, (2001) Why Schools Matter: a cross-national comparison of curriculum and learning. San Francisco: Jossey-Bass
Stigler, J. and Hiebert, J. (1999) The Teaching Gap: Best Ideas from the World's Teachers for Improving Education in the Classroom. New York: The Free Press.
Tang, S and Zhang, F. (1998) Geometry in China: the teaching material. In: C. Mammana and V. Villani (eds.) Perspectives on the Teaching of Geometry for the 21st Century, An ICMI Study [Chapter 7.2]. The Netherlands: Kluwer Academic Publishers.
Valverde, G. A. et al, (2002) According to the Book: using TIMSS to investigate the translation of policy into practice through the world of textbooks. Dordrecht: Kluwer Academic Press.
Villani, V. et al (1994), Perspectives on the Teaching of Geometry for the 21st Century (Discussion Document for an ICMI Study), L'Enseignement Mathematique, 40(3-4), 345-357. Reprinted in C. Mammana and V. Villani (eds.) (1998) Perspectives on the Teaching of Geometry for the 21st Century, An ICMI Study [appendix]. The Netherlands: Kluwer Academic Publishers.
Page updated 26 March 2008
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