The order of theorems in the teaching of Euclidean geometry: Learning from developments in textbooks in the early 20th Century

The question of the order of theorems in geometry teaching is very important and it was one of the central issues in the early 20th Century in England Employing ideas from the methodological framework proposed by Schubring (1987), the order of theorems in the geometry textbooks written by Godfrey and Siddons is analysed within their pedagogy and social context. The main foci for this analysis areElementary Geometry (1903) andA Shorter Geometry (1912), which were widely used in secondary schools at that time. The theorems in these textbooks were arranged differently from those of Euclid'sElements Godfrey claimed the order was organised from an general educational point of view. InA Shorter Geometry, flexibility concerning the order of theorems was recognised as a revision fromElementary Geometry. The analysis presented in this paper provides us with information about teaching practice at that time, for example that teachers might still be bound by examinations after 1903, and helps us to understand important aspects of dealing on the order of theorems in geometry teaching.

[1]  D. E. Smith.  The teaching of elementary mathematics , 1900 .

[2]  C. Godfrey.  Is There Need of a Recognized Sequence in Geometry , 1907 .

[3]  H. S. Carslaw.,et al.  The Teaching of Mathematics , 1912, Nature.

[4]  C. Godfrey.  Geometry Teaching: The Next Step , 1920 .

[5]  The Annual Meeting of the Mathematical Association—Report of the Council for 1925 , 1926 .

[6]  A. W. Siddons,et al.  The Teaching of Elementary Mathematics. , 1932 .

[7]  Progress. Presidential Address to the Mathematical Association, January 1936 , 1936 .

[8]  Chauncey D. Leake,et al.  British Association for the Advancement of Science , 1953, Science.

[9]  L. Roth,et al.  Modern Geometry , 1961, Nature.

[10]  New Mathematics 3 , 1969 .

[11]  H. F. Baker,et al.  The Teaching of Geometry in Schools , 1971 .

[12]  Elementary Geometry. By C. Godfrey, M.A., and A. W. Siddons, M.A., 3s. 6d. (Cambridge University Press.)A School Geometry. Pt. III. (Circles, 1s.) By H. S Hall and F. H Stevens (Macmillan & Co.) , 1971 .

[13]  A. Howson.  Milestone or Millstone? , 1973, The Mathematical Gazette.

[14]  Charles Godfrey (1873–1924) and the reform of mathematical education , 1973 .

[15]  Understanding Mathematics--A Perennial Problem? Part 4. , 1975 .

[16]  Michael H. Price,et al.  Squared paper in the nineteenth century: Instrument of science and engineering, and symbol of reform in mathematical education , 1980 .

[17]  A history of mathematics education in England: Notes , 1982 .

[18]  G. Howson.  A history of mathematics education in England: Subject index , 1982 .

[19]  Gert Schubring,et al.  On the Methodology of Analysing Historical Textbooks: Lacroix as Textbook Author. , 1987 .

[20]  S. Hagard.  England , 1995, The Knight and the Blast Furnace.

[21]  D. Quadling.  A century of textbooks , 1996 .

[22]  Vinicio Villani,et al.  Perspectives on the teaching of geometry for the 21st century : an ICMI study , 1998 .

[23]  T. Fujita.  The study of elementary geometry (1903) by Godfrey and Siddons (1):roles of experimental tasks in the teaching of geometry , 2001 .

[24]  Robertson Davies,et al.  THE BRITISH EXPERIENCE , 2003 .

[25]  The Teaching of Mathematics in Public Schools , Nature.