“What renders a problem definite, and what leaves it indefinite, may best be understood from mathematics. The very important idea of solving a problem within limits of error is an element of rational culture, coming from the same source. The art of totalizing fluctuations by curves is capable of being carried, in conception, far beyond the mathematical domain, 65 where it is first learned. The distinction between laws and coefficients applies in every department of causation. The theory of Probable Evidence is the mathematical contribution to Logic, and is of paramount importance.”

Source: Education as a Science, 1898, pp. 151-152.

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Alexander Bain7

Scottish philosopher and educationalist 1818–1903

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E. W. Hobson (1856–1933) British mathematician

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“Teachers need to be trained on how children learn, not only how to solve mathematical problems. They must know how to make learners well understand the New Math and enable them to solve mathematical problems.”

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“This is not what I thought physics was about when I started out: I learned that the idea is to explain nature in terms of clearly understood mathematical laws; but perhaps comparisons are the best we can hope for.”

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Source: Education as a Science, 1898, p. 153.

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