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The place of experimental tasks in geometry teaching: learning from the textbook designs of the early 20th century

By Taro Fujita and Keith Jones


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. <br/><br/>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"

Topics: LB1603, LB2361
Year: 2003
OAI identifier: oai:eprints.soton.ac.uk:11247
Provided by: e-Prints Soton

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  2. (1998). A Model for Analysing the Transition to Formal Proofs in Geometry, In: A. Oliver and K. Newstead (Eds),
  3. (1912). A Shorter Geometry. Cambridge: doi
  4. (2001). A Translational Comparison of Primary Mathematics Textbooks: The case of multiplication, doi
  5. (2002). According to the Book: Using TIMSS to Investigate the Translation of Policy into Practice Through the World of Textbooks.
  6. (2002). An Investigation of Mathematics Textbooks and their Use in English, French and German Classrooms: who gets an opportunity to learn what?, doi
  7. (1998). Deductive and Intuitive Approaches to Solving Geometrical Problems, In:
  8. (2001). Education and Employment: doi
  9. (1903). Elementary Geometry: practical and theoretical. Cambridge:
  10. (2002). Establishing a Custom of Proving in American School Geometry: evolution of the two-column proof in the early twentieth century,
  11. (1932). Geometry and the Imagination (translated by P. doi
  12. (1975). Geometry and the Universities: Euclid and his modern rivals 1860 – doi
  13. (1952). Godfrey and Siddons. Cambridge: doi
  14. (1995). Mathematical Screen Metaphors, In: doi
  15. (1994). Mathematics for the Multitude?
  16. (1999). Mathematics Textbooks Across the World: Some Evidence from the Third International Mathematics and Science Study.
  17. (1976). Mathematisation as a Pedagogical Tool, [reprinted
  18. (1908). Modern Geometry. Cambridge: doi
  19. (1956). New York: Chelsea Publishing Co. [reprinted edition,
  20. (1997). On the Difficulties met by Pupils in Learning Direct Plane Isometries, In: E. Pehkonen (Ed),
  21. (1987). On the Methodology of Analysing Historical Textbooks: Lacroix as Textbook Author,
  22. (1998). Perspective on the Teaching of Geometry for the 21st Century. doi
  23. (1920). Practical and Theoretical Geometry. Cambridge:
  24. (1991). Questions about Geometry, In:
  25. (1909). Solid Geometry. Cambridge: doi
  26. (1999). Student’s Performance in Proving: Competence or Curriculum?, In:
  27. The Annual Meeting of the doi
  28. (1988). The Awareness of Mathematization. Educational Solutions: New York. [also available as chapters 10–12
  29. (1998). The British Experience, In:
  30. (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.
  31. (1931). The Teaching of Elementary Mathematics. Cambridge: doi
  32. (1902). The Teaching of mathematics, doi
  33. (1993). The Theory of Figural Concepts. doi
  34. (1913). The Value of Science, In: doi
  35. (1976). Understanding Mathematics: a perennial problem? Part 3,
  36. (2000). What are Essential to Apply the Discovery Function of Proof in Lower Secondary School Mathematics?, In:

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