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One of the important problems in secondary instruction in mathematics is to find concrete material for vitalizing the work in elementary algebra and geometry. Frequently the work as given is too abstract for the student, and does not connect closely with his experience. Since the road to the abstract is over the concrete, it is hoped that the illustrative material here offered will make the student's approach to generalized mathematics easier by using much arithmetical work.

The Realschulen of Germany originated in a reactionary movement against the humanistic studies. One fundamental idea in the starting of the Realschulen was preparation for commercial professions, while the humanistic institutions prepared for the learned ones. In the course of time, however, the Realschutlen have enlarged their curriculum to meet the demands of general culture.

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(1914). An Application of Partial Derivatives to the Ellipse. The American Mathematical Monthly: Vol. 21, No. 1, pp. 15-17.

The subject of indeterminate forms is usually treated in algebra or in calculus; and hence it seldom occurs to the student that these forms may occur in trigonometry. It is sometimes desirable to examine critically some of the operations in proving identities, so that a false conclusion may not be drawn. Frequently the process of dividing both numerator and denominator by a factor holds only for certain values of the variable, or variables, involved. The occasional presence of indeterminates in solving spherical triangles teaches us that a spherical triangle is not always determined when three parts are given, as is sometimes supposed.

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