Unterrichtsblätter für Mathematik und Naturwissenschaft (1904), p. 128.
[505]. Indeed, the aim of teaching [mathematics] should be rather to strengthen his [the pupil’s] faculties, and to supply a method of reasoning applicable to other subjects, than to furnish him with an instrument for solving practical problems.—Magnus, Philip.
Perry’s Teaching of Mathematics (London, 1902), p. 84.
[506]. The participation in the general development of the mental powers without special reference to his future vocation must be recognized as the essential aim of mathematical instruction.—Reidt, F.
Anleitung zum Mathematischen Unterricht an höheren Schulen (Berlin, 1906), p. 12.
[507]. I am of the decided opinion, that mathematical instruction must have for its first aim a deep penetration and complete command of abstract mathematical theory together with a clear insight into the structure of the system, and doubt not that the instruction which accomplishes this is valuable and interesting even if it neglects practical applications. If the instruction sharpens the understanding, if it arouses the scientific interest, whether mathematical or philosophical, if finally it calls into life an esthetic feeling for the beauty of a scientific edifice, the instruction will take on an ethical value as well, provided that with the interest it awakens also the impulse toward scientific activity. I contend, therefore, that even without reference to its applications mathematics in the high schools has a value equal to that of the other subjects of instruction.—Goetting, E.
Ueber das Lehrziel im mathematischen Unterricht der höheren Realanstalten; Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 2, p. 192.
[508]. Mathematics will not be properly esteemed in wider circles until more than the a b c of it is taught in the schools, and until the unfortunate impression is gotten rid of that mathematics serves no other purpose in instruction than the formal training of the mind. The aim of mathematics is its content, its form is a secondary consideration and need not necessarily be that historic form which is due to the circumstance that mathematics took permanent shape under the influence of Greek logic.—Hankel, H.
Die Entwickelung der Mathematik in den letzten Jahrhunderten (Tübingen, 1884), p. 6.