It is this characteristic that suggests the term cumulative as descriptive of the plan of the series.

6. Recognition of Differences in Ability of Children.

It is possible for all normal children to learn the fundamental facts of arithmetic. Some will learn them much more quickly than others. Some will be able to solve more difficult problems than others. The Modern Arithmetics furnish material adapted to these various grades of ability. It is as grievous an error to permit the stronger pupils to pass along by meeting merely the minimum requirement, as to expect the weaker ones to perform tasks beyond their ability.

SUGGESTIONS TO TEACHERS

THE work of the fifth and sixth grades, by pretty general agreement throughout the country, embraces these topics:

1. All operations with integers.

2. Common fractions.

3. Decimals.

4. Common measurements.

5. Percentage, without special applications.

Besides practice in the mere elements and technique of these topics, it is expected that pupils will have enough practical applications to give them facility in the solution of common, everyday problems that are usually met by people in the ordinary walks of life.

Pupils should often be reminded that only a few principles need be mastered and that these few occur again and again during the arithmetic course, in new applications.

The absence of extended reductions, addition, subtraction, multiplication, and division of compound numbers is intentional. These operations are seldom used in real life. When children know the tables and are trained to visualize the conditions given in a problem, they should be able to make any simple one-step reduction that may be required.

Let "cases" and special processes be put aside, relying upon the simple statement of the problem in every case to indicate the solution. The oral exercises should never be assigned for study outside the recitation period. These exercises, studied in class with the pupils, furnish the teacher's golden opportunity for teaching. If anything must be omitted, let it be the written rather than the oral exercises. Teachers of these grades should know thoroughly the work of preceding grades, so that there may be no confusion on account of change of methods.

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