Herbart s Recognition Theory of Basic Figures: Through a Comparison with Pestalozzi s Learning Theory Tadayuki KISHIMOTO Faculty of Human Development,
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1 Herbart s Recognition Theory of Basic Figures: Through a Comparison with Pestalozzi s Learning Theory Tadayuki KISHIMOTO Faculty of Human Development, University of Toyama The purpose of this paper is to re-construct Herbart s recognition theory of basic figures in comparison with Pestalozzi s recognition theory. It is shown that Pestalozzi s ideas were based on Kant s philosophy as follows; number corresponds to the concept of time, and figure to the concept of space. Herbart s ideas were based on combination theory or trigonometry, which was popular in Europe during the 19th century. Therefore, Pestalozzi decided on a square as the basic figure, whereas Herbart chose a triangle. We could therefore draw an outline of Herbart s recognition theory of basic figures by using the perspectives for discussing Pestalozzi s learning theory as follows; (1) Method of positional decision, (2) Use of construction materials, (3) Importance of naming. Key words: Herbart, Pestalozzi, basic figure, triangle, and mathematics education Johann Friedrich Herbart, Johann Heinrich Pestalozzi, a ABC ABC b c a Herbart, a
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3 Vol. No. b a Pestalozzi, ABC ABC ABC ABC Pestalozzi, b
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5 Vol. No. Blass b Herbart, ABC ABC Herbart, b J.J. Tranchot K.L.v. Lecoq Herbart, b x sin x; cos x; tang x
6 a b a b c d e ab ac Herbart, b a
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8 Herbart, a ABC Blass, J. L. (1982): Padagogische Theoriebildung bei Johann Friedrich Herbart, Meisenheim am Glan. Herbart, J. F. (a): Über Pestalozzi s neueste Schrift: Wie Gertrud thre Kinder Lehrte. An drei Frauen., in Sämtliche Werke, hrsg, von K. Kehrbach und O. Flugel, Band.,,. SW Herbart, J. F. (b): Pestalozzi s Idee eines ABC der Anschauung, in SW., Band.,,. J. F. ABC Herbart, J. F. (1802c): Pestalozzi, Heinrich, Wie Gertrud thre Kinder lehrte in Briefen, in SW., Band. 12, 5 8, Herbart, J. F. (1803): Pestalozzis Elementarbucher in SW., Band. 12, 8 14, Herbart, J. F. (1804a): Über den Standpunkt der Beurteilung der Pestalozzi schen Unterrichtsmethode, in SW., Band. 1, , Herbart, J. F. (): Allgemeine Padagogik aus dem Zweck der Erziehung abgeleitet, in SW., Band.,,. J. F. Herbart, J. F. (): Umriss Pädagogischer Vorlesungenin, SW., Band.,,.J. F.,.,.,.,. Kant, I. (): Kritik der reinen Vernunft,, Immanuel Kants Werke, hrsg. von E. Cassirer usw, Bd,. I. F. F. F. E.,,. P. Pestalozzi, J. H. (): Wie Gertrud thre Kinder Lehrte, Gesämmelte Werke, hrsg. von H. Stettbacher, usw. Bd,. J. H.. ABC,. W.
9 Vol. No.,.,. Wagemann, B. (1957): Quadrat-Dreieck-Kugel : die Elementarmathematik und ihre Bedeutung fur die Padagogik bei Pestalozzi, Herbart und Frobel. Weinheim : Julius Beltz. Willmann, O. (): Didaktik als Bildungslehre nach ihren Beziehungen zur Sozialforschung und zur Geschichte der Bildung mit einer Einfuhrung von Professor Dr. Fr. X. Eggersdorfer in Otto Willmanns Leben und Werk, Verlag Herder Wien.O. kisimoto@edu.u-toyama.ac.jp
Die Stelle des Begriffs Interesse in Bildungslehre von Eggersdorfer, F. X. Shinichi Ushida 1 Herbart, J. F. Reformpädagogik Erziehender Unterricht Ben
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