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FOR INDUCTIVE TEACHING, DRILLING

AND TESTING

BOOK NUMBER FIVE

Common and Decimal Fractions, Mensuration, Denominate

Numbers, Business Transactions

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NOTE TO TEACHERS.

THE attention of teachers is called to the following features of this series of books - features which should be kept in mind as the various subjects are presented.

1. The separation of teachers' and pupils' books, whereby pupils may be taught properly and may not be given too great assistance. Suggestions as to methods of teaching and drilling, as well as the illustrative processes, explanations, rules, and definitions which belong to the teacher to develop analytically are put into the Teachers' Manual, while in the pupils' books are presented only such exercises as are needed for practice.

2. The careful gradation of problems, by which pupils acquire inductively a knowledge of arithmetical relations and principles, and skill in arithmetical processes. This is in recognition of the well-known pedagogical principles of proceeding from the known to the unknown, and from the simple to the complex. It is advised that this plan be kept constantly in mind by the teacher, and that whenever a process is not understood or is not readily performed, the pupils should be taken back to processes which are well known and which can be performed readily, and then should be led forward by easy steps until the desired end is reached.

3. Frequent reviews, and such an arrangement of exercises as will enable pupils to have needed practice in the applications of each principle, first by itself, and afterwards in connection with other principles which have been learned.

4. The large amount of oral work, or work which may be done without the aid of figures. Three objects of Mental Arithmetic are sought in these exercises : (a) Illustration of principles and a preparation for written work, (6) Development of the logical powers, (c) Cultivation of ability to work with large numbers by short processes

5. The great number and variety of problems. The aim has been to give the largest number of problems that will be needed for teaching and for drilling in all grades. For this reason, and because the forms of expression are varied, being taken from many sources, there will be no necessity of giving supplementary drill lessons on the blackboard. Blackboard lessons are objectionable not only on account of a waste of the teachers' time and strength, but also on account of the injury done to pupils' eyes in much reading and copying from the blackboard.

6. Practicalness of work in respect to the character of the problems, and the solution of them. Care has been taken to give problems which are most likely to be met in every-day life, and to give them in a practical form. Many of the miscellaneous review problems were made by mechanics, clerks, accountants, etc., with a view of presenting conditions most likely to occur.

7. The introduction of statistics and facts of physics, astronomy, history, geography, etc., thus enabling pupils to gain incidentally much useful information.

8. The use of drill tables and other devices to save the time of teachers.

In addition to the above features, some of which are distinctively new so far as American text-books are concerned, there is the separation of pupils' exercises for practice into small books somewhat on the lines of gradation in City graded schools. By this arrangement there are gained greater convenience of handling and economy of wear than in the use of a large book which is intended to be used for several years by the same pupil.

The first Section of this book is given to a review of some work included in Book No. 4. If it is found too difficult for pupils, a review with objects and by the development method should be made.

Operations with fractions previously carried to twelfths and thousandths are continued in Sections II, III and IV. If the previous work has been well done, little objective teaching will be found necessary beyond representations that may be made by drawings. Whenever any difficulty is met in performing these exercises, reference should be made to similar exercises with halves, thirds, tenths, hundredths, etc., using objects when neces

sary. Mensuration also is continued in Section V, advancing to the measurement of all polygons and of rectangular solids. It is advised that so far as possible diagrams be drawn in illustration or explanation of problems. Teachers are reminded that constructive work with blocks is needed at this stage.

In addition to the graded and illustrative work indicated for the introduction of new measures, it will be advisable to teach such measures objectively.

In making out bills, receipts, cash accounts, etc., it will be better for pupils to draw the needed rulings, rather than to use blanks provided for the purpose.

For methods of teaching the various subjects and for answers to problems see Teachers' Manual which is designed to accompany all books of the series.

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