Fujita, Taro and Jones, Keith (2003) The place of experimental tasks in geometry teaching: learning from the textbook designs of the early 20th century. Research in Mathematics Education, 5, (1&2), 47-62.
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Abstract

The dual nature of geometry, in that it is a theoretical domain and an area of practical experience, presents mathematics teachers with opportunities and dilemmas. Opportunities exist to link theory with the everyday knowledge of pupils but the dilemmas are that learners very often find the dual nature of geometry a chasm that is very difficult to bridge. With research continuing to focus on understanding the nature of this problem, with a view to developing better pedagogical techniques, this paper examines the place of experimental tasks in the process of learning geometry.

In particular, the paper provides some results from an analysis of innovative geometry textbooks designed in the early part of the 20th Century, a time when significant efforts were being made to improve the teaching and learning of geometry. The analysis suggests that experimental tasks have a vital role to play and that a potent tool for informing the design of such tasks, so that they build effectively on pupils’ geometrical intuition, is the notion of the geometrical eye, a term coined by Charles Godfrey in 1910 as “the power of seeing geometrical properties detach themselves from a figure".

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References in Article

Arzarello F., Micheletti C., Olivero F., Robutti O.: 1998, A Model for Analysing the Transition to Formal Proofs in Geometry, In: A. Oliver and K. Newstead (Eds), Proceedings of 22nd Annual Meeting of the International Group for the Psychology of Mathematics Education. Stellenbosch. Vol 2, pp.24-31.
Atiyah, M.: 2001, Mathematics in the 20th Century: Geometry versus Algebra, Mathematics Today, 37(2), 46-53.
Brock, W. H.: 1975, Geometry and the Universities: Euclid and his modern rivals 1860 – 1901, History of Education, 4, 21-35.
Clausen-May, T., Jones, K., McLean, A. and Rollands, S.: 2000, Perspectives on the Design of the Geometry Curriculum, Proceedings of the British Society for Research into Learning Mathematics, 20 (1&2), 34-41.
Department for Education and Employment: 2001, Key Stage 3 National Strategy: Framework for Mathematics. London: DfEE.
Fischbein, E.: 1993, The Theory of Figural Concepts. Educational Studies in Mathematics, 24(2), 139-162.
Fischbein, E: 1994, The Interaction between the Formal, the Algorithmic and the Intuitive Components in a Mathematical Activity, In: R. Biehler et al (eds), Didactics of Mathematics as a Scientific Discipline. Dordrecht: Reidel, pp 231-245.
Foxman, D.: 1999, Mathematics Textbooks Across the World: Some Evidence from the Third International Mathematics and Science Study. Slough: NFER.
Gattegno, C.: 1988, The Awareness of Mathematization. Educational Solutions: New York. [also available as chapters 10–12 of Science of Education, part 2B]
Godfrey, C.: 1910, The Board of Education Circular on the Teaching of Geometry, Mathematical Gazette, 5, 195-200.
Godfrey, C. and Siddons, A. W.: 1903, Elementary Geometry: practical and theoretical. Cambridge: Cambridge University Press.
Godfrey, C., Siddons, A. W.: 1908, Modern Geometry. Cambridge: Cambridge University Press.
Godfrey, C. and Siddons, A. W.: 1909, Solid Geometry. Cambridge: Cambridge University Press.
Godfrey, C. and Siddons, A. W.: 1912, A Shorter Geometry. Cambridge: Cambridge University Press.
Godfrey, C. and Siddons, A. W.: 1920, Practical and Theoretical Geometry. Cambridge: Cambridge University Press.
Godfrey, C. and Siddons, A. W.: 1931, The Teaching of Elementary Mathematics. Cambridge: Cambridge University Press.
Griffiths, H. B.: 1998, The British Experience, In: Mammana, C. and Villani, V. (Eds). Perspectives on the Teaching of Geometry for the 21st Century, An ICMI Study. Netherlands: Kluwer Academic Publishers, pp.194-204.
Haggarty, L. and Peppin, B.: 2002, An Investigation of Mathematics Textbooks and their Use in English, French and German Classrooms: who gets an opportunity to learn what?, British Educational Research Journal, 28(4), 567-590.
Healy, L. and Hoyles, C.: 1999, Student’s Performance in Proving: Competence or Curriculum?, In: I. Schwank (ed.). Proceedings of the First Conference of the European Society for Research in Mathematics Education. Vol. 1, pp. 153-166.
Herbst, P. G.: 2002, Establishing a Custom of Proving in American School Geometry: evolution of the two-column proof in the early twentieth century, Educational Studies in Mathematics, 49(3), 283-312.
Hilbert, D. and Cohn-Vossen, S.: 1932, Geometry and the Imagination (translated by P. Nemenyi). New York: Chelsea Publishing Co. [reprinted edition, 1956]
Howson, A. G.: 1982, A History of Mathematics Education in England. Cambridge: CUP.
Hoyles, C., Foxman, D. and Küchemann, D.: 2002, A Comparative Study of Geometry Curricula. London: Qualifications and Curriculum Authority.
Jones, K.: 1998, Deductive and Intuitive Approaches to Solving Geometrical Problems, In: C. Mammana and V. Villani (Eds.), Perspective on the Teaching of Geometry for the 21st Century. Dordrecht: Kluwer, pp78-83.
Jones, K., Gutiérrez, A, and Mariotti, M. A. (Eds): 2000, Proof in Dynamic Geometry Environments, a special issue of Educational Studies in Mathematics, 44(1&2).
MA.: 1902, The Annual Meeting of the Mathematical Association, Mathematical Gazette, Vol. II. No. 31, pp. 129-143.
Malara, N. and Iaderosa, R.: 1997, On the Difficulties met by Pupils in Learning Direct Plane Isometries, In: E. Pehkonen (Ed), Proceedings of 21st Annual Meeting of the International Group for the Psychology of Mathematics Education. Helsinki. Vol 3, 208-215.
Mammana, C. and Villani, V. (Eds.): 1998, Perspective on the Teaching of Geometry for the 21st Century. Dordrecht: Kluwer.
Mason, J. 1991, Questions about Geometry, In: D. Pimm and E. Love, (Eds.), Teaching and Learning School Mathematics, Hodder and Stoughton, London, pp77-90.
Mason, J. and Heal, B. 1995, Mathematical Screen Metaphors, In: R. Sutherland and J. Mason (Eds.), Exploiting Mental Imagery with Computers in Mathematics Education, NATO ASI Series F Vol 138, Springer, Berlin, pp 291-308.
Miyazaki, M.: 2000, What are Essential to Apply the Discovery Function of Proof in Lower Secondary School Mathematics?, In: T. Nakahara and M. Koyama (Eds), Proceedings of 24th Annual Meeting of the International Group for the Psychology of Mathematics Education. Hiroshima: Hiroshima. Vol. 4, pp.1-8.
Perry, J.: 1902, The Teaching of mathematics, Educational Review, Vol. XXIII, pp. 158-189.
Poincaré, H.: 1913, The Value of Science, In: H. Poincaré, The Foundations of Science (trans. G. B. Halstead). New York: Science Press.
Price, M. H.: 1976, Understanding Mathematics: a perennial problem? Part 3, Mathematics in School, 5, 18-20.
Price, M. H.: 1994, Mathematics for the Multitude? – A history of the Mathematical Association, Leicester: Mathematical Association.
Price, M. H.: 2001, England, In Grinstein, L.S. and Lipsey, S.I. (Eds.) Encyclopedia of Mathematics Education. Routledge Falmer, pp. 216-218.
Quadling, D.: 1996, A Century of Textbooks. Mathematical Gazette, 487, 119-126.
Royal Society/Joint Mathematical Council: 2001, Teaching and Learning Geometry 11-19, London, Royal Society/Joint Mathematical Council.
Schubring, G.: 1987, On the Methodology of Analysing Historical Textbooks: Lacroix as Textbook Author, For the Learning of Mathematics, 7(3), 41-51.
Siddons, A. W.: 1952, Godfrey and Siddons. Cambridge: Cambridge University Press.
Sutherland, R., Winter, J. and Harries, T.: 2001, A Translational Comparison of Primary Mathematics Textbooks: The case of multiplication, In: C. Morgan and K. Jones (Eds). Research in Mathematics Education, vol. 3, pp. 155-167.
Valverde, G. A.: 2002, According to the Book: Using TIMSS to Investigate the Translation of Policy into Practice Through the World of Textbooks. Dordrecht: Kluwer.
Wheeler, D.: 1976, Mathematisation as a Pedagogical Tool, [reprinted 2001] For the Learning of Mathematics, 21(2), 50-53.