Excerpt from The Thorndike Arithmetics, Vol. 2

How much is two thirds of $75 less 10% of itself is how much? And What percent of 40 is 32? These exercises in equation form with missing numbers are harder than routine drills with question and answer, but are more productive of ability, and of ability of a higher type. They also penalize mere memoriter acquisition and serve as an ideally clear, brief, and unrestricted form for mental imagery of arithmetical facts and relations. Their value as preparation for the use of formulae in shop arith metic and for algebra is obvious.

The meanings of decimal numbers are taught directly from an extension of the thousands, hundreds, tens, ones series to tenths, hundredths, and so on, as well as from the comparison with film, and roim The latter is used chie¿y to emphasize the smallness of the magnitudes and the commensurability of the two sorts of expressions, and to clarify the general concept of a fraction by experience with fractions with very large denomina tors. Experience shows that place value, United States money, and railroad distance tables are more useful in explaining decimal numbers than the unfamiliar 1335, films, and fins.

The placing of the decimal point in division by a decimal num ber is taught as a consequence of two general rules: Divisor X quotient must =dividend, (number of decimal places in the divisor) (number of decimal places in the quotient) must (number of decimal places in the The special devices by which correctness may be secured are made secondary to full mastery of the general principle and surety in deciding where the decimal point must be in simple cases without the help of any device. The justification for this is the fact that the devices themselves are of little importance, and the common custom of treating them as the essence of the procedure in dividing by a decimal degrades arithmetic to a mere collection of recipes.

In using this book, the best results will be obtained by follow ing its plan closely except for changes authorized by the super visor in charge of Grades V and VI. Each section contributes something definite toward the growth of arithmetical ability. In many cases the work has as its chief aim the preparation for later acquisitions, or the use together of abilities already acquired separately, or the adaptation of an ability to special difficulties. The abilities and interests which the pupils have, as well as those which they are to acquire, are also considered in arranging the problems and exercises. Consequently, the organization is more subtle than it is in texts in which the pupil learns first to add frac tions, then to apply the adding of fractions to problems, then to subtract fractions, then to apply the subtracting of fractions to problems, and so on. The organization in this book, though less obvious, will be found more effective in producing in the learner a steady integration of habits and powers into a total arithmetical ability which will meet life's needs.

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