On the Study and Difficulties of Mathematics (Chicago, 1898), chap. 1.
[431]. The instruction of children should aim gradually to combine knowing and doing [Wissen und Können]. Among all sciences mathematics seems to be the only one of a kind to satisfy this aim most completely.—Kant, Immanuel.
Werke [Rosenkranz und Schubert], Bd. 9 (Leipzig, 1838), p. 409.
[432]. Every discipline must be honored for reason other than its utility, otherwise it yields no enthusiasm for industry.
For both reasons, I consider mathematics the chief subject for the common school. No more highly honored exercise for the mind can be found; the buoyancy [Spannkraft] which it produces is even greater than that produced by the ancient languages, while its utility is unquestioned.—Herbart, J. F.
Mathematischer Lehrplan für Realgymnasien, Werke [Kehrbach], (Langensalza, 1890), Bd. 5, p. 167.
[433]. The motive for the study of mathematics is insight into the nature of the universe. Stars and strata, heat and electricity, the laws and processes of becoming and being, incorporate mathematical truths. If language imitates the voice of the Creator, revealing His heart, mathematics discloses His intellect, repeating the story of how things came into being. And the value of mathematics, appealing as it does to our energy and to our honor, to our desire to know the truth and thereby to live as of right in the household of God, is that it establishes us in larger and larger certainties. As literature develops emotion, understanding, and sympathy, so mathematics develops observation, imagination, and reason.—Chancellor, W. E.
A Theory of Motives, Ideals and Values in Education (Boston and New York, 1907), p. 406.
[434]. Mathematics in its pure form, as arithmetic, algebra, geometry, and the applications of the analytic method, as well as mathematics applied to matter and force, or statics and dynamics, furnishes the peculiar study that gives to us, whether as children or as men, the command of nature in this its quantitative aspect; mathematics furnishes the instrument, the tool of thought, which we wield in this realm.—Harris, W. T.
Psychologic Foundations of Education (New York, 1898), p. 325.