THE PLACE OF EXPERIMENTAL TASKS IN GEOMETRY TEACHING: LEARNING FROM THE TEXTBOOK DESIGNS OF THE EARLY 20^th CENTURY

References

• Arzarello , F. , Micheletti , C. , Olivero , F. and Robutti , O.: . 1998 . “ A Model for Analysing the Transition to Formal Proofs in Geometry ” . In Proceedings of 22nd Annual Meeting of the International Group for the Psychology of Mathematics Education , Edited by: Oliver , A. and Newstead , K. 24 – 31 . Stellenbosch. Vol 2 .
   Google Scholar
• Atiyah , M.: . 2001 . Mathematics in the 20th Century: Geometry versus Algebra . Mathematics Today , 37 ( 2 ) : 46 – 53 .
   Google Scholar
• Brock , W. H.: . 1975 . Geometry and the Universities: Euclid and his modern rivals 1860 –1901 . History of Education , 4 : 21 – 35 .
   Google Scholar
• 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 .
   Google Scholar
• Department for Education and Employment . 2001 . Key Stage 3 National Strategy: Framework for Mathematics , London : DfEE .
   Google Scholar
• Fischbein , E.: . 1993 . The Theory of Figural Concepts . Educational Studies in Mathematics , 24 ( 2 ) : 139 – 162 .
   Google Scholar
• Fischbein , E.: . 1994 . “ The Interaction between the Formal, the Algorithmic and the Intuitive Components in a Mathematical Activity ” . In Didactics of Mathematics as a Scientific Discipline , Edited by: Biehler , R. 231 – 245 . Dordrecht : Reidel .
   Google Scholar
• Foxman , D.: . 1999 . Mathematics Textbooks Across the World: Some Evidence from the Third International Mathematics and Science Study , Slough : NFER .
   Google Scholar
• Gattegno , C. 1988 , The Awareness of Mathematization . Educational Solutions: New York, [also available as chapters 10–12 of Science of Education, part 2B]
   Google Scholar
• Godfrey , C.: . 1910 . The Board of Education Circular on the Teaching of Geometry . Mathematical Gazette , 5 : 195 – 200 .
   Google Scholar
• Godfrey , C. and Siddons , A. W.: . 1903 . Elementary Geometry: practical and theoretical , Cambridge : Cambridge University Press .
   Google Scholar
• Godfrey , C. and Siddons , A. W.: . 1908 . Modern Geometry , Cambridge : Cambridge University Press .
   Google Scholar
• Godfrey , C. and Siddons , A. W.: . 1909 . Solid Geometry , Cambridge : Cambridge University Press .
   Google Scholar
• Godfrey , C. and Siddons , A. W.: . 1912 . A Shorter Geometry , Cambridge : Cambridge University Press .
   Google Scholar
• Godfrey , C. and Siddons , A. W.: . 1920 . Practical and Theoretical Geometry , Cambridge : Cambridge University Press .
   Google Scholar
• Godfrey , C. and Siddons , A. W.: . 1931 . The Teaching of Elementary Mathematics , Cambridge : Cambridge University Press .
   Google Scholar
• Griffiths , H. B.: . 1998 . “ The British Experience ” . In Perspectives on the Teaching of Geometry for the 21st Century, An ICMI Study , Edited by: Mammana , C. and Villani , V. 194 – 204 . Netherlands : Kluwer Academic Publishers .
   Google Scholar
• Haggarty , L. and Pepin , 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 .
   Web of Science ®Google Scholar
• Harris , M.: . 1997 . Common Threads: Women, Mathematics and Work , Stoke-on-Trent : Trentham Books .
   Google Scholar
• Healy , L. and Hoyles , C.: . 1999 . “ Student's Performance in Proving: Competence or Curriculum? ” . In European Research in Mathematics Education I , Edited by: Schwank , I. 153 – 166 . vol 1 .
   Google Scholar
• 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 .
   Google Scholar
• Hilbert , D. and Cohn-Vossen , S. 1932 , Geometry and the Imagination (translated by P. Nemenyi) . New York : Chelsea Publishing Co . [reprinted edition, 1956]
   Google Scholar
• Howson , A. G.: . 1982 . A History of Mathematics Education in England , Cambridge : CUP .
   Google Scholar
• Hoyles , C. , Foxman , D. and Küchemann , D.: . 2002 . A Comparative Study of Geometry Curricula , London : Qualifications and Curriculum Authority .
   Google Scholar
• Jones , K.: . 1998 . “ Deductive and Intuitive Approaches to Solving Geometrical Problems ” . In Perspective on the Teaching of Geometry for the 21st Century , Edited by: Mammana , C. and Villani , V. 78 – 83 . Dordrecht : Kluwer .
   Google Scholar
• Jones , K. Gutiérrez , A and Mariotti , M. A. 2000 , Proof in Dynamic Geometry Environments, a special issue of Educational Studies in Mathematics , 44(1&2) .
   Google Scholar
• Langley , E. M. 1903 , Review of'Elementary geometry' and'A school geometry' , Mathematical Gazette , Vol. II, p. 369 [reprinted Vol. LV. (1971), pp. 239–40] .
   Google Scholar
• Mathematical Association: . 1902 . The Annual Meeting of the Mathematical Association, Mathematical Gazette, II . No. , 31 : 129 – 143 .
   Google Scholar
• Malara , N. and Iaderosa , R.: . 1997 . “ On the Difficulties met by Pupils in Learning Direct Plane Isometries ” . In Proceedings of 21st Annual Meeting of the International Group for the Psychology of Mathematics Education , Edited by: Pehkonen , E. 208 – 215 . Helsinki. Vol 3 .
   Google Scholar
• Mammana , C. and Villani , V. 1998 , Perspective on the Teaching of Geometry for the 21st Century . Dordrecht : Kluwer .
   Google Scholar
• Mason , J.: . 1991 . “ Questions about Geometry ” . In Teaching and Learning School Mathematics , Edited by: Pimm , D. and Love , E. 77 – 90 . Hodder and Stoughton, London .
   Google Scholar
• Mason , J. and Heal , B.: . 1995 . “ Mathematical Screen Metaphors ” . In Exploiting Mental Imagery with Computers in Mathematics Education, NATO ASI Series F , Edited by: Sutherland , R. and Mason , J. 291 – 308 . Vol 138, Springer, Berlin .
   Google Scholar
• Miyazaki , M.: . 2000 . “ What are Essential to Apply the Discovery Function of Proof in Lower Secondary School Mathematics? ” . In Proceedings of 24th Annual Meeting of the International Group for the Psychology of Mathematics Education”. Hiroshima: Hiroshima Edited by: Nakahara , T. and Koyama , M. Vol. 4 , 1 – 8 .
   Google Scholar
• Perry , J. 1902 , The Teaching of mathematics , Educational Review , XXIII , 158 – 189 .
   Google Scholar
• Poincaré , H. 1913 , The Value of Science , In: H. Poincaré , The Foundations of Science (trans. G. B. Halstead) . New York : Science Press .
   Google Scholar
• Price , M. H.: . 1976 . Understanding Mathematics: a perennial problem? Part 3 . Mathematics in School , 5 : 18 – 20 .
   Google Scholar
• Price , M. H.: . 1994 . Mathematics for the Multitude?-A history of the Mathematical Association , Leicester : Mathematical Association .
   Google Scholar
• Price , M. H.: . 2001 . “ England ” . In Encyclopedia of Mathematics Education , Edited by: Grinstein , L.S. and Lipsey , S.I. 216 – 218 . Routledge Falmer .
   Google Scholar
• Quadling , D.: . 1996 . A Century of Textbooks . Mathematical Gazette , 487 : 119 – 126 .
   Google Scholar
• Royal Society/Joint Mathematical Council : 2001 , Teaching and Learning Geometry 11–19 , London, Royal Society/Joint Mathematical Council .
   Google Scholar
• Schubring , G.: . 1987 . On the Methodology of Analysing Historical Textbooks: Lacroix as Textbook Author . For the Learning of Mathematics , 7 ( 3 ) : 41 – 51 .
   Google Scholar
• Siddons , A. W.: . 1952 . Godfrey and Siddons , Cambridge : Cambridge University Press .
   Google Scholar
• Sutherland , R. , Winter , J. and Harries , T.: . 2001 . “ A Transnational Comparison of Primary Mathematics Textbooks: The case of multiplication ” . In Research in Mathematics Education Edited by: Morgan , C. and Jones , K. Vol. 3 , 155 – 167 .
   Google Scholar
• 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 .
   Google Scholar
• Wheeler , D.: . 1976 . Mathematisation as a Pedagogical Tool . reprinted 2001] For the Learning of Mathematics , 21 ( 2 ) : 50 – 53 .
   Google Scholar