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The Development of the Teaching of Geometry in Germany

Published online by Cambridge University Press:  03 November 2016

Georg Wolff*
Affiliation:
Düsseldorf (Germany)

Extract

[At the evening meeting of the Annual Meeting of the Mathematical Association on 5th January, 1937, Mr. A. W. Siddons took the chair, and in calling upon Professor Wolff for his paper said: Professor Georg Wolff came to England in 1913, and I believe I am right in saying that Harrow was the first school to which he came and that the last educational institute he was at in England was this Institute of Education in Southampton Row, where he talked with Sir Percy Nunn. When he was in England on that occasion Professor Wolff spent much of his time learning about the teaching of mathematics in this country. He has more recently been lecturing at Columbia University, New York.]

Type
Research Article
Copyright
Copyright © Mathematical Association 1937

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References

Page 82 of note * Siddons, A. W., “Progress”, Presidential Address to the Mathematical Association, January, 1936. The Mathematical Gazette, No. 237, 1936, p. 7 Google Scholar.

Page 82 of note † Wolff, , Georg, , Der Mathematische Unterricht der höheren Knabenschulen in England. B. G. Teubner, Leipzig, 1915 Google Scholar.

Page 83 of note * Fletcher, W C., Elementary Geometry. London, Edward Arnold CrossRefGoogle Scholar.

Page 82 of note † Godfrey, C., and Siddons, A. W., Elementary Geometry. Cambridge, 1903 Google Scholar.

Page 84 of note ‡ Board of Education, Special Reports on Educational Subjects, Vols. 26 and 27 The Teaching of Mathematics in the United Kingdom, Parts I and II. London, 1912.

Page 84 of note * Garstang, T. J., Parallel Straight Lines and the Method of Direction. Report of the International Commission, Vol. I, p. 274 Google Scholar.

Page 84 of note † Cambridge University Press.

Page 85 of note * Gerhardt, C. J., Leibniz, G. W., Mathematische Schriften, Bd. 7, p. 141 ff. Halle a. d. Saale, 1849-63.

Page 85 of note † ABC der Anschauung oder Anschauungslehre der Massverhältnisse.

Page 85 of note ‡ Herbart placed the triangle in the foreground.

Page 85 of note § Diesterweg, A., Leitfaden für den ersten Unterricht in der Formen—Grössen und räumlichen Verbindungslehre. Elberfeld, 1822 Google Scholar.

Page 85 of note ‖ Harnisch, W., Die Raumlehre oder die Messkunst, gewöhnlich Geometrie genannt. Berlin, 1821 Google Scholar.

Page 85 of note ¶ Ohm, G. S., Grundlinien zu einer zweckmässigen Behandlung der Geometrie. Erlangen, 1817 Google Scholar.

Page 86 of note * Wolff, Georg, Mathematik und Malerei, 2. Aufl. B. G. Teubner, Leipzig: p. 49.

Page 86 of note † Perspectiva. Frankfurt, 1614.

Page 86 of note ‡ Perspectiva Communis, 1 ed. Mailand, 1492, later appeared in Nürnberg in 1542.

Page 87 of note * Priestley-Klügel, , Geschichte u. gegenwärtiger Zustand der Optik. Leipzig, 1775 Google Scholar. Priestley, J., A familiar introduction to the Theory and Practice of Perspective. London, 1770 Google Scholar.

Page 88 of note * The best introduction to this very complex problem may be found in Ernst Tiedge, Bildungsaufgaben des mathematisch naturwissenschaftlichen Unterrichts der höheren Schulen. M. Diesterweg, Frankfurt, a.M., 1933.

Page 90 of note * Klein, F., Vorträge über mathematischen Unterricht, bearbeitet von Rud. Schimmack. B. G. Teubner, Leipzig, 1907 Google Scholar; Schimmack, , Rud., Die Entwicklung der mathematischen Unterrichtsreform in Deutschland. B. G. Teubner, Leipzig, 1911 Google Scholar.

Page 90 of note † Schimmack, when delivering his inaugural lecture (1911), laid historical foundation to this fusion. See Zeitschrift für math. und naturwissenschaftlichen Unterricht, Vol. 42, 1911, p. 569.

Page 97 of note * Reidt-Wolff-Kerst, Die Elemente der Mathematik. 4 Hefte Arithmetic, 4 Bände: Algebra, Analysis, Analytische Geometrie, Geometrie. G. Grote, Berlin, Dessauerste.

Page 97 of note † Kerschensteiner, G., Wesenu. Wert d. naturwissenschaftlichen Unterrichts, 1. Aufl., 1913, 3. Aufl., 1928, B. G. Teubner, Leipzig CrossRefGoogle Scholar.

Page 97 of note ‡ Siddons-Vassal, , Practical Measurements. Cambridge University Press, 1912 Google Scholar.

Page 97 of note § Richtlinien für die Lehrpläne an den höheren Schulen in Preussen, Weidmann, Berlin, 1925.

Page 98 of note * Hjelmslev, H., “Die Geometrie der Wirklichkeit”, Acta Mathematica, Vol. 40, 1915, pp. 3566 CrossRefGoogle Scholar; Hjelmslev, H., “Die natürliche Geometrie”, Abhandlungen aus dem Math. Seminar der Hamburger Universität, Vol. 2, 1933, p. 1, obtainable from B. G. Teubner, Leipzig Google Scholar.

Page 98 of note † It may be mentioned that U.S.A. has the same tendency. The extremely excellent book of Smith-Reeve-Morss, Text and Tests in Plane Geometry, Ginn and Co., New York and London, is a very good example in this direction.